deviation of coulomb’s

Deviation of Coulombs Force from the Force of Electrostatic Interaction between two conducting

Spheres

Dragia Ivanov, Yordan Epitropov, Stefan Bozhkov, Kiril Kolikov

Faculty of Physics and Faculty of Mathematics and Informatics

Plovdiv University

Plovdiv, Bulgaria

[email protected]

AbstractThe magnitude of the force of electrostatic interaction

between two point charges is determined by applying Coulombs law. However, in practice two charged bodies with certain

dimensional size, geometrical shapes and physical structures

interact rather than two point charges. This causes the problem

for evaluating the deviation of the Coulombs force from the force of electrostatic interaction between two charged bodies to

emerge. We consider this problem for two charged spheres with

arbitrary radiuses and arbitrary electrical charges based on the

derived by us exact analytical formula for the force of

electrostatic interaction between them.

Keywords-law; conducting sphere; force of electrostatic

interaction; absolute inaccuracy; relative inaccuracy

INTRODUCTION

Coulombs law determines the magnitude of the force

21 2 04CF QQ R of electrostatic interaction between two point charges

1Q and 2Q which are at a distance R between

each other [1, 2, 3]. In practice, however, two charged bodies with certain sizes, geometrical shapes and physical structures interact rather than point charges. This causes the problem for

evaluating the deviation of Coulombs force CF from the

actual force F of electrostatic interaction between two electrically charged bodies. We solve this problem for two conducting spheres with arbitrary charges and arbitrary radiuses.

The problem for determining the electrostatic force of interaction between two charged conducting spheres with arbitrary radiuses and charges is considered for the first time by Poisson. Later on this research is considerably simplified by Sir Thompson (Lord Kelvin) with the introduced by him theory of image charges.

This problem is also looked into by Maxwell [1]. It is precisely him who discovers that the electrostatic force between two spheres is different than the electrostatic force given by Coulombs law between point charges with the same sizes, located at the centres of the spheres. According to Maxwell this deviation is caused by the redistribution of the charges as a result of the mutual electrostatic influence. He

suggests a general method for determining the force of interaction between two spheres with arbitrary charges and radiuses using zonal harmonics with complex mathematical apparatus [1].

Smythe applies the method of image charges for determining the electrostatic force between two spheres which are not intersecting with arbitrary charges and radiuses [4] by using hyperbolical functions. He computes the first few terms in a sum describing the force by the capacities of the spheres. Saranin [5] computes more concrete results using Smythes approach.

Jackson [6] does not reach a concrete solution of this problem in the general case but using the method of the image charges he describes the way for solving of the problem for two spheres which do not intersect with different radiuses and charges by showing how the induced charges and their locations can be determined iteratively.

For the first time we derive an exact analytical formula for the electrostatic force of interaction between two conducting

spheres 1S and 2S with arbitrary charges 1Q and 2Q and

arbitrary radiuses 1r and 2r , respectively [7].

Let R be the distance between the centres 1O and 2O of

the spheres 1S and 2S in inertial system J . As the charges 1Q

and 2Q are uniformly distributed on the surfaces of 1S and 2S

we assume that before the interaction of the spheres they are

concentrated in the centres 1O and 2O , respectively.

As a result of the electrostatic interaction between 1S and

2S on their surfaces some induced charges, respectively 1Q

and 2Q , appear which are interconnected. Then on the surfaces

of 1S and 2S there are some uniformly distributed charges 1Q

and 2Q left, and given by the law of preservation of the electric

charge the following equations hold

1 1 1Q Q Q and 2 2 2Q Q Q . (1)

The current research is done with the financial support of the Fund Scientific Studies of the Bulgarian Ministry of Education, Youth and Science as part of the contract DTK 02/35.

SECTION10. Natural science (mathematics, chemistry, biology, physics)

Advanced Research in Scientific Areas 2012December, 3. - 7. 2012

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Formally, we can assume that 1Q and 2Q are located on the

segment 1 2OO as well as 1Q and 2Q are concentrated at the

centres 1O and 2O of the spheres.

We determine the charges 1Q and 2Q by using the method

of image charges [1, 8] and from (1) we determine the charges

1Q and 2Q . As a result of iQ ( 1,2i ) the image charges ,i jQ

( 1,2,3,...j ) are generated.

Let i ir R ( 1,2i ). In [7] we assume that the binomial

coefficient 10

n

for every whole number n and introduce

for 1,2,3,...j the following denominations

2 21, 1 21 0

11 1

j kk k s s

j

k s

j s j k sA

k s s

,

222, 1 21 0

11 1

j kk k ss

j

k s

j s j k sA

k s s

,

2 21, 1 21 0

1 1j k

k k s s

j

k s

j s j k sB

k s s

,

222, 1 21 0

1 1j k

k k ss

j

k s

j s j k sB

k s s

. (2)

We denote with ,i jd ( 1,2i ; 1,2,3,...j ) the distance

from the charge ,i jQ to the centre 1O or 2O of the sphere in

which ,i jQ lies. Then we prove the following

1, 12

1,2 1 2

1, 1

m

m

m

Ad R

B

, 1, 12

1,2 1

1,

m

m

m

Bd R

A ,

2, 12

2,2 1 1

2, 1

m

m

m

Ad R

B

, 2, 12

2,2 2

2,

m

m

m

Bd R

A . (3)

Furthermore, we establish that

1

1 2

1,2 1 1

1, 1

m m

m

m

Q QB

, 1 21,2 11,

m m

m

m

Q QA

,

1

1 2

2,2 1 2

2, 1

m m

m

m

Q QB

, 1 22,2 22,

m m

m

m

Q QA

. (4)

Moreover, in [7] we define

1 21

1 1,

m m

m m

XA

, 1 221 2,

m m

m m

XA

,

1

1 2

1

1 1, 1

m m

m m

YB

, 1

1 2

2

1 2, 1

m m

m m

YB

, (5)

where 0 1i when 0i ( 1,2i ) and we get

1 2 2 2

1

1 2 1 2

1

1 1

Q X Q YQ

X X YY

,

2 1 1 1

2

1 2 1 2

1

1 1

Q X QYQ

X X YY

. (6)

Based on (4-6) the image charges ,i jQ

( 1,2i ; 1,2,3,...j ) are determined.

We denote the charges from (4) which are located in the

sphere 1S with jQ and the ones located in the sphere

2S with jQ ( 0,1,2,...j ). So 1,0 01Q Q Q and

2,0 02Q Q Q , and for 1,2,3,...m we have 2,2 1 2 1m mQ Q ,

1,2 2m mQ Q and 1,2 1 2 1m mQ Q , 2,2 2m mQ Q . Their respective

distances from (3) we denote with jd and jd ( 0,1,2,...j ).

Then, if j jd R and j jd R according to Coulombs

law for the magnitude F of the projection of the force of

interaction onto 1 2OO acting in spheres 1S and 2S we get

2 2

0 00

1

4 1

j i

j ij i

Q QF

R

. (7)

CONNECTION BETWEEN COULOMBS FORCE AND THE ACTUAL ELECTROSTATIC FORCE FOR CONDUCTING SPHERES WITH

NON-ZERO CHARGES

As in [7 and 9] we will determine the coefficient of proportionality between the force of interaction between two spheres and Coulombs force.

If two spheres have non-zero charges 1 0Q and 2 0Q

and 2 1Q Q k then from (6) follows that 111Q Q L ,

222Q Q L where

2 211 2 1 2

1=(1 )(1 )

X kYL

X X YY

,

1

1 12

1 2 1 2

1=(1 )(1 )

X k YL

X X YY

. (8)

From (4) and (6) we obtain that , ,i j i i jQ QL for 1,2i

and 1,2,3,...j where for 1,2,3,...m we have

1

1 2

1,2 1 1

1, 1

=m m

m

m

L LB

, 1 21,2 11,

=m m

m

m

L LA

,

1

1 222,2 1

2, 1

=m m

m

m

L kLB

, 2,2

212,2 = Lk

AL

m

mm

m

. (9)

Let us denote

0 1L L , 2 1 2,2 1m mL L , 2 1,2m mL L and

0 2L L , 1

2 1 1,2 1m mL k L

, 12 2,2m mL k L

. (10)




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Figure 1. Graphics of F depending on R given

different values of k

Figure 2. Graphics of CF and F depending on R when

1

4k .

Figure 3. Graphics of CF and F depending on R when 1

4k .

Then (7) can be written in the following form

1 2

2 20 00

=4 1

j i

j ij i

L LQQF

R

, i.e. CF F L , (11)

where the coefficient

2

0 0 1

j i

j ij i

L LL

is caused by the

geometry of the two spheres.

Example 1. Let 1S and 2S be two electrically charged

conducting spheres with equal radiuses 21 2 2 10r r

m.

Based on (11) on Fig. 1 we present a family of graphics of the

force F of electrostatic interaction between 1S and 2S

depending on the distance R between the centres of the

spheres 1O and 2O , respectively. The graphics are made using

different ratio k between their charges 2Q and 1Q ,

respectively:

2 1 1,1 2,1 4,1 8,0, 1 8, 1 4, 1 2, 1k Q Q .

We can observe that when 1 2Q Q we get 0F and

when 2 0Q , 1 0Q or when the charges are of different

types (a positive one and a negative one) we get 0F .

However, when the charges 1 2Q Q are of the same type (both

positive or both negative) we get 0F , 0F or 0F

depending on R , while Coulombs force 0CF is always

either only positive (of retraction) or only negative (of attraction).

On Fig. 2 and Fig. 3 the graphics of CF are collated with

the graphics of F depending on R for the case of charges of

the same type (both positive or both negative) when 1 4k

and the case of charges of different types (a positive one and a

negative one) when 1 4k . Coulombs force CF is

determined for point charges 1Q and 2Q located at the centres

1O and 2O of the spheres.

As shown by the graphics the idealised Coulombs force

0CF either strictly increases or strictly decreases with the

decreasing of the distance R according to the law 2~1CF R .

When 1 4k with the decreasing of the distance R the

force F is initially one of retraction and gradually increases, reaches a maximum and further decreases to zero. Afterwards it assumes negative values and as a force of attraction it quickly increases with further decreasing of R (Fig. 2). Obviously in this specific case the change of the actual force depending on R has very complex character and differs drastically from Coulombs force.

When 1 4k the force 0F is a force of attraction for

each R (Fig. 3) but also differs from 0CF .

In all cases the idealised Coulombs force CF for small

distances R with respect to the sum of the radiuses 1r and 2r




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Figure 4. Graphics of the absolute inaccuracy CF depending on k given

spheres with equal radiuses and different R

Figure 5. Graphics of the relative inaccuracy C

C

F

F

depending on k given

spheres with equal radiuses and different R

deviates strongly from the actual force F . Only when the distance R is sufficiently large then both spheres can be assumed to be point objects and the actual force and

Coulombs force are practically equal. Moreover, CF F for

each 1 2R r r . This result follows from the redistribution of

the charges on the surfaces of the two spheres 1S and 2S

caused by the electrostatic interaction between them.

In each particular case comparison between Coulombs

force CF and the actual force F can be made using (7).

I. ABSOLUTE AND RELATIVE INACCURACIES OF COULOMBS FORCE FROM THE FORCE OF ELECTROSTATIC

INTERACTION BETWEEN CONDUCTING SPHERES

If one charge is zero and the other not, for example

1 0Q and 2 0Q , then Coulombs force between them is

0CF , whereas the actual force of interaction F between the

spheres 1S and 2S assumes very large absolute values when

0k according to the graphics from Fig. 1. This shows that in this case Coulombs law cannot at all describe the actual electrostatic interaction.

When 1 0Q and 2 0Q from (11) follows that the

absolute inaccuracy CF of Coulombs force CF with respect

to the force of electrostatic interaction F between the

conducting spheres 1S and 2S is

. 1C C CF F F F L . (12)

Then the relative inaccuracy C CF F of CF with respect

to F is

1C

C

FL

F

. (13)

The coefficient

2

0 0 1

j i

j ij i

L LL

is non-dimensional

variable depending only on 1r , 2r , R and 2 1k Q Q . The

variable L is actually a function describing the effect of redistribution of the charges on the surfaces of the spheres. Moreover, from (12) and (13) follows that the closer L is to 1 the smaller the absolute and relative inaccuracies are, and vice versa.

According to (8-10) L is a function of the ratio k . That is

why we can express the absolute and relative inaccuracies of

CF as functions of k .

Example 2. On Fig. 4 and Fig. 5 the dependence of the

absolute and relative inaccuracies as functions of the ratio k

are graphically shown. In all of the graphics the spheres are

with equal radiuses 21 2 2 10r r

m and the distance

between their centres from the top to the bottom is,

respectively, 24.5 10R m, 25 1 0R m and 26.5 10R m.

In this case one can see that the absolute inaccuracy CF

has a single local minimum. The relative inaccuracy C CF F

has a single minimum when 1k , i.e. when 1 2Q Q .

Moreover, when the spheres are charged with equal charges the

smallest value of C CF F is reached when the spheres are

with equal radiuses.

Let us point out that the absolute and relative inaccuracies can also be expressed as functions of the distance R as well as

functions of 1r and 2r . We will only look into C CF F R

and C C C CF F F F R .

Example 3. On Fig. 6 and Fig. 7 for spheres with radiuses 2

1 2 10r m and 22 1 10r

m and 1 4k and

1 4k the graphics of CF and C CF F are presented

depending on the distance R .

One can see that 0CF and 0C CF F when the

distance R is relatively large with respect to the sum of the




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Figure 6. Graphics of CF depending on R given spheres with different

radiuses and 1

4k ,

1

4k .

Figure 7. Graphics of C

C

F

F

depending on R given spheres with different

radiuses and 1

4k ,

1

4k

radiuses 1r and 2r . This way the actual force F between

charged spheres given large distances R with respect to 1 2r r

is practically equal to Coulombs force CF as earlier shown by

the type of graphics on Fig. 2 and Fig. 3.

From Fig. 6 and Fig. 7 one can also see that the absolute and relative inaccuracies are smaller if both the spheres are charged with the same type (both positive or both negative) of charges.

II. DISCUSSION

Given relatively small distances R with respect to the sum

of the radiuses 1r and 2r of two conducting spheres the force

of electrostatic interaction F between the spheres is different

from the electrostatic force CF between point charges with the

same sizes located at the centres of the spheres defined by

Coulombs law. This deviation of Coulombs force CF from

F is caused by the redistribution of the charges on the surfaces

of the spheres which is caused by the mutual electrostatic influence [1]. Moreover, given relatively large distances R it

can be practically assumed that CF F .

Our method for determining the deviation of the idealized

Coulombs force CF for point charges 1Q and 2Q from the

actual force F of electrostatic interaction between two spheres

with charges 1Q and 2Q can be also applied for determining

the deviation of the energy of the connection and the potential

of the field generated by 1Q and 2Q according to [7, (17) and

(18)].

Moreover, other bodies which have centres of symmetry can be considered by reducing them to spheres with the same areas of the surfaces.

We use these results in our research of the electrostatic interaction between the nucleons in the nucleuses [10, 11, 12]. We reach the conclusion that Coulombs forces are comparable to the nuclear ones. This is caused by the forces of interaction between the pairs proton-neutron which turn out to be acting in the short range, whereas, the forces of interaction between the pairs proton-proton are in turn determined to be acting in the long range [13].

III. CONCLUSION

The meaning of Coulombs law is practically applied in all fields within physics and makes this elementary in form and at the same time fundamental law one of the most useful scientific tools [2, 3]. This is precisely why the considered by us problem for determining the deviation of Coulombs force

CF from the force of electrostatic interaction F between two

conducting bodies is particularly important. The determined by

us deviation of CF from F in some particular cases is drastic

and shows how important in different practical situations it is to make such an evaluation of this deviation.

REFERENCES

[1] J. Maxwell, A Treatise on Electricity and Magnetism, vol. 1, Dover, 1954.

[2] D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics, Wiley, 2010.

[3] W. Rosser, Interpretation of Classical Electromagnetism, Kluwer Academic Publishers, 2010.

[4] W. Smythe, Static and Dynamic Electricity, McGraw-Hill, 1968.

[5] V. Saranin, On the interaction of two electrically charged conducting balls, Phys-Usp., vol. 42, pp. 385-390, 1999.

[6] J. Jackson, Classical Electrodynamics, Wiley, 1998.

[7] K. Kolikov, D. Ivanov, G. Krastev, Y. Epitropov and S. Bozhkov, Electrostatic interaction between two conductive spheres, J. Electrostat, vol. 70, pp. 91-96, 2012.

[8] B. Budak, A. Samarskii and A. Tikhonov, A Collection of Problems in Mathematical Physics. Dover Publications, 1988.

[9] K. Kolikov, D. Ivanov, G. Krastev, Y. Epitropov and S. Bozhkov, Erratum to Electrostatic interaction between two conducting spheres, J. Electrostat. vol. 70, pp. 91-96, 2012.

[10] K. Kolikov, D. Ivanov and G. Krustev, Electromagnetic nature of the nuclear forces and a toroid model of nucleons in atomic nuclei, Natural Sciense, vol. 4, pp. 47-56, 2012.




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[11] K. Kolikov, D. Ivanov and G. Krustev, Electromagnetic nature of the nuclear forces and toroid structure of the deuteron and triton, Natural Sciense, vol. 4, pp. 123-130, 2012.

[12] K. Kolikov, Electromagnetic nature of nuclear forces and the toroid structure of the helion and the alpha particle, Natural Sciense, vol. 4, pp. 484-491, 2012.

[13] D. Ivanov and K. Kolikov, Short-range action and long-range action of the electrostatic forces within atomic nuclei (unpublished)




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SECTION 1. Business ManagementIT Outsourcing Risks: Empirical Evidence from Bulgarian Service ProvidersThe model of a catholic CSR in comparison with the model of a laic CSRCompany Cooperation to Retain and Develop the Knowledge of Women on Child-Care Leave (Based on Hungarian Studies)Evidence of Shareholder Activism and Information Deficiency in the Listed Property Sector in South AfricaDeterminants of Spanish purse seine fleet survival: effects of fisheries subsidiesStrategic Factor Analysis Summary- Applicability in the Case of City Tourism in Novi Sad (Serbia)An Epistemological Challenge of Psychological Traps Presence in Financial ReportingDifferences in interests of inhabitants and business sector: case study of airing in Liepaja, LatviaCorporate Social Responsibility contra Green WashingA Survey of the Talent Management Practices in Bulgarian Restaurants

Management of autonomous employees groups Strategic Management of Companies as a Model for Social EnterprisesSocial Entrepreneurship in PolandImpact of the change of human resources on customer satisfaction in a hospital dialysis unitEcotourism Management in Kazakhstan Critiques About Shared Service Model Firm level heterogeneity: Main research topicsIndustry analysis and strategic groups: A theoretical and empirical reviewTheoretical and Practical aspects of Performance Management in Poland and across the globeMOTIVATION OF WORK AS AN ELEMENT OF MANAGERIAL PROCESS BY THE BANK PERSONNELLogistics and Supply Chain Management as a Field of InterdisciplinarityCriticism of transnational corporations on the example of developing countriesTheoretical frameworks on supplier relationship management in entreprise economy The role of human resource management in the period of recessionSupply Chain Management in renewable energy networksKnowledge and absorptive capability: Are they relevant for achieving above average performance?(e)-Entrepreneurship, digital competences and employability

SECTION 2. MarketingPhysical Experiment for The influence of The Human Bio field on The use-value of The product in The new Marketing ParadigmONLINE MARKETING TOOLS AND THEIR IMPACT ON IMAGE OF ORGANIZATIONNext Green PortsCognitive MarketingMarketing Activities of Polish BanksFacebook: A new weapon for Greek Politicians? An investigative study in the Greek political era

Cognitive dissonance in healthcare: A conceptual frameworkUsage of the Multidimensional Scaling in Exploring a Firm's Image and Competitiveness Co-creation and ethical issues: the case of Altromercato communityWord-Of-Mouth Marketing Usage with Comparison of Turkish Culture in TurkeySkills, users, and communities in value creation processAssessment of Validity of Data Regulated by the Communication-Law - an Example Based on the Austrian Print Media Market

SECTION 3. Economy and Business EconomicsThe Customs Union of the Eurasian Economic Community: Analysis of Regional IntegrationHuman resources development and growth of SMEs: key facts and figures for RomaniaForecasting the Care Expenditures of the Dependent Elderly PopulationStature and life-time labor market outcomes: Accounting for unobserved differencesValuing Real Estate as Contractual Cash-Flow with a Put-OptionProblems of Linear Least Square RegressionTheoretical Aspects of Shadow Economy StudyForeign Aid Flow and Real Exchange Rate in Albania The restructuring of the Spanish fishing sector after the end of the agreement between the European Union and Morocco and its consequences on employmentEVALUATION OF INSTITUTIONAL CHANGES EFFECTIVENESS IN THE FOREST INDUSTRY OF RUSSIAStatistical analysis of the factors which take effect on the new HUF credit volume in the SME sector Valuation Under Uncertainty Using Regression Techniques The Objective Necessity of Supporting Small and Medium Businesses in GeorgiaEthics and Economics: The Case of Food Safety in Spanish Meat Sector Impact of Government Financial Security on Economic GrowthNon-depository financial institutions and Shadow Banking SystemThe Analysis of Financial Conglomerates Development in the Czech Republic over the Last Five YearsFlat Tax and Progressive Tax in AlbaniaInitial public offerings in China and IndiaDoes really, the new international political situation has changed the role of economic instruments?Economic Crisis Impact upon Franchise Business in Romania Regional convergence in Spain, 1980-2003:Effects of the economic crisis on migrants' remittancesThe Evolution of Labor Market Institutions in Post-Socialist EconomiesDevelopment of the economic systems theory and the competitiveness concept based on self-organizationThe Impact on Economic Development and Employment of the Various Categories of Transport InfrastructureInnovations in Czech ICT companiesFacility Management and IT SupportProduction and consumption of biofuels in Castile and Leon regionTrade specialization of Central and Eastern European CountriesAccess to technology: an alternative strategy to reduce the size of the informal sectorCosting in Passenger Air Transport and the Use of Managerial Decision Making in the Tariff DestinationMonetary policy committees and the use of unconventional monetary policy instruments\PRICE WAR:WINNER AND LOSERS IN EXTRA-VIRGIN OLIVE OILFactors Affecting Investment Attractiveness of Regions: The Case of Latvia Aspects of the Institutional Economics in enhancing the Countrys CompetitivenessMedia and the StateMeasuring the Relationship Between Divisions of Medium-high-tech Sector in Opolskie VoivodshipDemographic and Financial Risk Measures of Implicit Pension DebtImpact of Universal Consumer Consciousness on Structure of Gross Domestic Product: Theoretical Discussion The role of Jnos Kdr in the Hungarian attempts to join the International Monetary FundEconomic growth, public expenditures and competitiveness of European economies under the impact of the economic crisissisfEvolutionary analogies in economics: development, structure, optimizationConcepts of polycentrism and its determination in urban system of Latvia

SECTION 4. Public service, LawThe main problems of interaction between authorities and small business in regional economy STAGES OF FORMATION AND HISTORICAL DEVELOPMENT OF THE INSTITUTE OF NECESSARY DEFENSE IN THE REPUBLIC OF KAZAKHSTANPublic policy and the law defraud in the interntional private lawPPPs and new urban centralities activationLand Ownership Acquisition by Natural Persons and Legal Entities, under the Conditions of Romania's Accession to the European UnionThe role of the Internet In the Polish Parliamentary Elections in 2011Seasonality of the urban toll system in StockholmThe domicile of natural personsWORKING TIME AND INTERNAL FLEXIBILITY OF EMPLOYMENT RELATIONSProcedural Peculiarities in the Consideration of Matter of Natural persons InsolvencyThree-dimensional marks as community trade marksThe commitment to graduate employability in higher education institutions. Usefulness and Imperfections of the Small Claims Procedure, in the New Code of Civil Procedure Adopted in RomaniaThe position and the role of direct democracys institutions in the political system of Principality of AndorraEvolution of the voting system in the electoral process of the Roman PontiffChanging by knowledgeThe Principle of Material Publicity of the Land RegisterThe need for multi-stakeholder cooperation on road traffic safetyFORENSIC INVESTIGATION OF COMPUTER CRIME (CYBERCRIME)Undercover investigatorConsiderations on the reform in public administration in RomaniaThe approach and coverage of offences of narcotics in the Albanian Criminal Code Electoral Rights in the Romanian Political SystemDiffusion of law: Class action in the Polish Civil Procedure Importance of forensic investigation to identify unknown persons and bodiesVICTIMOLOGICAL PREVENTION ONE WAY OF HELPING VICTIMS OF HUMAN TRAFFICKING IN LATVIA

SECTION 5. Financing and AccountingThe accounting problem of heritage assetsUtilization of quantile risk measures in measuring financial risk of non-financial companiesMaximizing the Sharpe RatioAbout the relations between Management Accounting Systems, Intellectual Capital and PerformanceProduct design in profit sharing life annuity systemsInflation Risk Model in a Defined Contribution Pension Scheme The Structure and Funding of Current Needs of University Students Financial dimension of measurement and assessment in the model of performance card for the hospitalsACCOUNTING CONCEPTS OF INCOME: EVIDENCE FROM SERBIABusiness process of innovation creation and commercialization of knowledgeHow to prevent distress in local government: a new model applied in ItalyMethods and Forms of Social Security Funding2011 EBA Stress Testing in Europe A precautionary approach in standard setting due process. The case of Public-Private PartnershipFinancing the counteraction of natural disasters effects in the Silesian Voivodeship (NUTS 2)Accounting Policies and Options from Companys True and Fair View to Fiscal, Management Concerns Emission rights and the financial reportsBUSINESS AND FINANCIAL DECISIONS BASED ON INFORMATION PROVIDED BY ACCOUNTING INFORMATION SYSTEMSThe Application of Management Accounting (Controlling) Instruments in Small and Medium Size Enterprises in Nord-Western Croatia Determinants of capital structure: Evidence from Romanian manufacturing companiesFamily firms and corporate investment policy Accounting in the New Age

SECTION 6. Psychology, Sociology and Pedagogy, Social ScienceGAZE TRACKING METHOD USE IN THE SATISFACTION EVALUATION (MATLAB ENVIRONMENT) IN MARINE EDUCATIONEnglish language learning in adult groups with people 21 years and older:The Icarus Didactics Group. A challenge of teaching method of Diplomatics, Palaeography and Medieval HistoryThe spread of the Internet and the sociology of marriage: proposals for a research agendaMathematical language as a means of forming the mathematical culture of a future teacher Ethnic political parties versus multicultural paradigm Does ability-based emotional intelligence contribute to school achievement of elementary school pupils?Does the medium influence the message?Is Bologna the new Guernica of education? Intergenerational solidarity in Latvia: solidarity against older generation, its justificationThe analysis of errors in the solution of ordinary differential equationsMethodological Issues in Involuntary Autobiographical Memory ResearchStrawberry arouses forever?Teachers dynamics in the process of implementation of multicultural educational systemHERMENEUTICAL APPROACHES TO ORGANIZATIONAL COMMUNICATION IN RUSSIAOtherness and TogethernessBlending Theoretical Frameworks in the Analysis of Advertising Images of Europeanization Internet Addiction Disorder: Survey of a sample of University studentsJob-demands resources model and exhaustion: the role of flow-work enjoymentEvaluation of learning organized by employerLearning by Blogging: a Research on Educational Potential of BlogsSelected pathological inclinations in behavioral profile of serial killer LEISURE AND HIGH INTELLECTUAL ABILITIESInterpreters training peculiarities in polycultural environmentChanges of Values in Japanese people living in ItalyMASS MEDIA AND THE MANAGEMENT OF POLITICAL CRISIS DURING THE ELECTIONThe Food-Mediated Identity of Maghrebi Muslim Migrants in ItalyTHE HOSPITAL AS A PLACE OF MEMORY: THE REFUGE FOR INFANTILE PARALYSIS (OPORTO, PORTUGAL)The role of spirituality in the cessation of suicide ideation among the church-going youth in a rural community in the Limpopo Province, South AfricaModel of differentiated studies for securing an inclusive approach at the first stage of basic education in Latvia Social Work and migrant minors problems in Spain An investigation in to different dimensions of quality of life and factors related to it among cardiac patients after heart surgeryEducational Multimedia Space Factor in Reading Preparation for Children of Pre-school AgeOptimizing Methods and Technologies Used When Teaching Civil Engineering Students Mass Media Anthropology: a Post-modern Field of Research Andragogy Principles As Entry to University Instruction EnhancingDemocratization of global governance: from modern state to cosmopolitan governancePerspectives from Other PlacesAggressive behaviour phenomenon of our timePROBLEM OF PHENOMENON OF HAPPINESS IN PERSPECTIVE OF TODAY'S POSITIVE PSYCHOLOGYThe reception of social capital in the reality of challenges towards individual in XXI century Topicality of including work forms promoting self-understanding in the education process of visual art teachersThe Suffering Genie of GoetheManaging the cultural offering and guest spending in the hotelVirtual innovative environment of practices at Russian teacher-training university The social work as a professional perspective the students interest in social work as specialization of studyMemorials in citizenship education Bridges over troubled watersImpact of Comenius Assistantships in Choosing a Teaching CareerBiomaterials in the case study by on-line teachingRole of Practice in Developing International Cooperation Competence The origin of media education in Eastern Siberia and the Far EastSituational (in)consistency in learning strategiesHow to teach gender in a science-centered university course: de-constructing the identity paradigm of sexualityThe Social and Community MediationHope and Humor in Palliative Care Gender Differences in Self-Disclosure for the Unknown Person on the Internet CommunicationContextual learning as major technology in adult vocational trainingENVIRONMENT AND HOUSING MARKETUnderstanding the motivation for senior volunteeringCommon social problems among Street Children in India(Sporting) body language communicationThe role of relevant recent autobiographical events emotional valence on implicit measures of ethnic attitudes Cultivated personal potential - investment for happiness and healthTERRALABThe Endogenous Causes of TerrorismDistributed and Mobile Work in FinlandWithout ceremony and without papers Humor and Health Practitionaires StressA new approach: social logisticsA Teaching Innovation Project addressed to students of 2nd and 3rd Year of Primary Education Teaching Degree (Faculty of Sciences of Education. University of Lleida)Improving students ability to craft scientific explanationsThe relations between socio-demographical factors, irrational beliefs, adult insecure attachment style and marital satisfaction of Lithuanian married couplesBlended learning as a way to individualize English teaching to students of non-linguistic depatrments of higher educational institutionsKosovo and the Caucasus: A Domino EffectMeta-communication An Undesirable Circumstance JUNIOR SCIENCE - NURTURING CHILDRENS NATURAL INTEREST IN SCIENTIFIC KNOWLEDGE Entrepreneurship Education in Primary Education Departments. The case of the University of Western Macedonia in GreeceGreek families raising an adolescent with learning disabilities Children with mild intellectual disabilityrepresent their family About Applying Information Literacy Standardsin Bulgarian Higher EducationInfluences of subjective perception on critical incidents upon mental and physical healthTHE DISPLACED BLACK WOMEN IN THE ARMED CONFLICT IN COLOMBIA: SOME MEMOIRS OF THE VICTIMSBeyond Business Gamification ThinkingEmpathy of Music Teachers in Lithuania as a Problem of Her Professional Self-ActualizationBetween&Betwixt

SECTION 7. Art, Religion, History, PhilosophyEco-ethical Audit In the System Of the Environmental ManagementThe Lost Beauty of the Socio-Christian FellowshipMayan- qeqchireligious Syncretism. Between transculturality and cultural preservationAgeing cities Liberty, Equality, Fraternity Three Challenges to Rawlsian Difference PrincipleThe phenomenon of resonance in the Labyrinth of Ravne (Bosnia-Hezegovina)Representing cultural identity in art: Material Thinking through post-structuralist approachesSarduys Seguidillas: Alter-ing Poetic SpaceTransylvanian Traditional Housing Czechoslovakia in the 1950s and the Suicidal Behaviour of Politically Persecuted PersonsSocial security in Slovakia until the First World War The Art of Fostering a Dialogue with a Child in the Prose of Eduard UspenskyInformation literacy beyond information transferJawish Cemetery in Grigoriy Kanovichs WritingThe Akathistos hymn Rev. Dr. Dumitru Stniloae Background, context and development of an Orthodox ecclesiological synthesis Influences of the Council of Trent on the Seventeenth Century Orthodox Confession of the Catholic and Apostolic Eastern Church by Peter Mogilas The ordination of the deaconess in the Barberini gr. 366 EuchologionTo be a wholeDialectics, but not reductiveEthnic Segregation at the Romanian-Hungarian Border at the Dawn of the Cold War Prison ArchitectureFrench translators of the Divine Comedy in the 18th 19th centuries and the obscene language: between foreignizing and ethnocentric censorshipEaster 1916 in the trenchesOrigins of Business Economics and AccountancyThe relationship between architectural detail and light in contemporary architectureHistory and organizational change within Italian parliamentary administrationsThe identity of a city. Modern conversion of Karol Scheiblers post-industrial empire in Lodz

SECTION 8. LinguisticsLife Insurance Lexicography: Three Case StudiesWhich language do interpreters use in Consecutive Interpreting?Theoretical Proposal of Hybrid Analysis of Lexical Unit: LightUsing the statistical textual analysis in the Italian university offering databaseA preliminary study of learning strategies in foreign language instruction: students beliefs about strategy useKiswahili and ki-english: divergences and convergences in the linguistic scenario of contemporary KenyaUncertainty: Peculiarities of CategorizationChallenges of writing and publishing in indigenous languages and impact on rural developmentMeans of manipulation in the war newsTelevision Interpreting and its playful macro-functionPolitical Speeches And Text StructureMusic and Simultaneous Interpreting

SECTION 9. EcologyDepollution Costs;Evolution,Actors,Influence Factors Effect of environmental Variables on the Growth of Cyathura carinataFlooding - natural Phenomenon. How can hedge against it?The experience of European countries - Technique vs. ecologyEvaluation Study of environmental pilot Projects of Thessaly Region in Greece, for the international Program Free-MED-Rivers Spaces of Balance for the Mediterranean, with use of multicriteria Models, Data bases and statistical AnalysisInvestigation of Resistance to vertical static Compression of three Layer corrugated Paperboard Recreational Potential of Danube Region (Slovakia) and Astrakhan Region (Russia)Microeconomic Aspects of the renewable Energy Sources in the Republic of Croatia Personal Values as an Antecedent of Environmental BehaviorInfluence of selected Work Parameters of fan Flat nozzles technical Conditions on spray QualityUrban Code - Cultural Ecology and Urban EnvironmentEnergy Efficiency of Zoos: An Interdisciplinary Challenge with Special Benefits in Urban EnvironmentsEffect of Organochlorine Pesticides Usage on Water Quality of Tano River in the Asunafo South District of Brong Ahafo Region of GhanaEco-Semiotic - Ecological Meanings of Watercourses in Small CommunitiesAssessment of Factors influencing Lignin Content in Energy crop PelletsAnother Solutions existPreliminary Assessment of the Potential CO2 Sources and Sinks of the Eastern UkraineEco-driving and the Environment: the Views of Trainees in a School of pedagogical and technological EducationA genomic approach for identification of fungal genes involved in pentachlorophenol degradation The Ecosystem of the Environmental News beat in GreecePromotion of Safety in Forest OperationsMicrobiological and physic-chemical Characterization during chestnut Composting for sustainable Fertilization

SECTION 10. Natural science (mathematics, chemistry, biology, physics)Extensibility of locally given Isometries of pseudoriemannian ManifoldsRegeneration of WD-extra activated Carbon spent in Acid Dyes adsorption Process by Fentons ReagentBiotechnologic Methods in the Oil and Gas IndustryOn differential Inequality |u(x)+a2u(x)|

deviation of coulomb’s

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arbitrary charges

point charges

charged spheres

arbitrary electrical

deviation of coulombs

method of image charges

charged conducting spheres

arbitrary radiuses