ELECTRIC FORCE AND FIELD

SSC TOPIC 6.2

Name…………………

6.2 Electric force and field (3h)     Electric force and electric Field  

6.2.1 State that there are two types of electric charge. 1

6.2.2 State and apply the concept of conservation of charge. 2

6.2.3 Describe and explain the properties of conductors and insulators. 3 Students should explain the properties in terms of the freedom of

movement of electrons. 6.2.4 State Coulomb's law. 1  Students should be aware of the law in the forms    and    .  

 The use of vector addition to determine the net force on a charge due to two or more other charges is expected.  

6.2.5 Define electric field strength. 1  Students should understand the meaning of test charge.  6.2.6 Determine the electric field strength due to one or more point charges. 36.2.7 Draw and explain electric field patterns for different charge configurations. 3 Students should be familiar with a point charge, a charged sphere, two point charges and oppositely charged parallel plates. The latter includes edge effect. Students should be aware of the term radial field.6.2.8 Solve problems involving electric charges, forces and fields. 3  

Electrostatics Charge is that property of a

body that produces an electric force over a distance.

Fundamental unit of charge:

Charge on an electron, e = -16 10-19 CCharge on a proton, qp = 16 10-19 C

CONDUCTORS and INSULATORS

An insulator

Wood, polystyrene, air, hair, cloth, glass, resin, paper, mica, salt, leather, ebonite, certain plastics

A conductor

Metals, the human body and any damp material

A transfer of charge from one object to another by rubbing - one becomes -ve, the other +ve.,

Different substances have different affinities for electrons.

(a) A charged metal sphere and a neutral metal sphere.

(b) When connected by a good conductor (eg a metal) the charge will flow until it is evenly distributed.

(c) When connected by an insulator (wood) almost no charge is conducted

Coulomb’s Law It was found experimentally by

Coulomb in 1785 that-

Colorado- Electric fields

+ +

FORCE BETWEEN 2 CHARGESFORCE BETWEEN 2 CHARGES

+ +

FORCE BETWEEN 2 CHARGESFORCE BETWEEN 2 CHARGES

Double DistanceDouble Distance

Where k is called the Coulomb constant.k depends upon 1) system of units2) nature of medium

In S.I. units 41k

Where is the permittivity of the medium.For a vacuum,

229

0

10094

1k Cunit:Nm

If the value of the force between any two charges is F, determine the new value of force if

(a) the charge q1 is doubled(b) the distance of separation is

halved(c) the charge q2 is halved and the

distance of separation is doubled.

When several forces act on an object (call them F1, F2 etc), the net force Fnet on the object is the vector sum of all the forces acting on it.

We can use components to add vectors. A diagram is essential.

Electric Fields

Charged bodies exert forces on each other, even when they are not in contact. This “action at a distance” force is attributed to an electric field set up by the charges in the space around them.

Lines of Force

RulesRules 1)

2)

3)

4)

+

-

+ -

Colorado- Electric fields

G:\Physics2000\Physics 2000\Phys2000\index.html

http://members.nbci.com/Surendranath/FieldLines/FieldLines.html

+ +

+

-

++

--

Electric Field Strength

Note: The force on a negative charge in an electric field will be in a direction opposite that of the field.

Field Due To an Isolated Point Charge

Consider a small positive test charge +q, at a point P, a distance d, from a charge +Q:

+Q

+q

d

From Coulomb’s Law, force on +q is given by,

By definition of electric field, strength at P,

Putting two together

Determine the electric field strength at a point where a +100C charge experiences a force of 1.6 x 10-15N.

Calculate the force acting on a proton (1.6 x 10-19C) between 2 charged parallel plates where the electric field strength is 100 NC-1.

At what distance in air from a charge of + 10 C would there be an electric field of strength 100 NC-1?

+Q

X

E

2

1

dE

If d doubled then E x 1/22

E x 1/4

r 2r 3r 4r 5r 6r 7r 8rDistance in terms of charges radius

+Q+Q

+ -q1 q2

To determine the electric field strength at a point To determine the electric field strength at a point caused by 2 charges.caused by 2 charges.STEPS:STEPS:

Calculate E at the point created by each charge separately.Calculate E at the point created by each charge separately.

Add these 2 E’s together vectoriallyAdd these 2 E’s together vectorially

+ -q1 q2

E2

+ +q1 q2

+ ++q

+2q

+ -q1 q2

Potential energy and potential

Gravitational EP

What force does mass m experience

What work is necessary to move the mass m a height h

What is the increase in Ep of the mass. Work done on the mass = Increase in Ep (cons of energy principle)

Electrical EP

What force does charge q experience

What work is necessary to move the charge q a distance d against the field

What is the increase in Ep of the charge. Work done on the charge = Increase in Ep (cons of energy principle)

Eqmg

Potential energy and potential

Gravitational PotentialThe potential energy per unit mass at a point is called the GRAVITATIONAL POTENTIAL at that point

Eqmg

Electric PotentialThe potential energy per unit charge at a point is called the ELECTRIC POTENTIAL at that point

NOTE: This is for uniform fields only

Electric Potential Energy and Electric potentialElectric Potential Energy and Electric potentialThe electric potential energy of the charge q in the uniformuniform E field= work done in moving the charge from zero of potential energy to the point it occupies

EP=0

d

Electric potential at a point is defined to be the electric potential energy per unit charge at that point. Its symbol is V.

Units are joules per coulomb (J/C) or volts (V)

uniformuniform E field

d=1.0cm

Example: For the situation shown find

(1) the electrical potential energy of the charge

(2) the electrical potential of the point (electrical potential is independent of the size of the charge)

q=2.0x10-6C

E=1.0x102 NC-1

P 506 Ex 17-2 Electric field obtained from voltage. Two parallel plates are charge to a voltage of 50V. If the separation between the plates is 0.050m, calculate the electric field between them.

One volt :

One electron volt :.

+

-

60V

HL

EQUIPOTENTIAL LINESEQUIPOTENTIAL LINES

Equipotential lines are lines joining points at the same potential and electric fields can be mapped by drawing these lines. These equipotential lines

(1) join points at the same potential

(2) are at 90o to lines of force

(3) have no direction potential is a scalar quantity

(4) are drawn so that there is a constant difference in potential between successive lines, and so their spacing gives an indication of field strength (the closer the lines, the stronger the field)

HL

Work done when charge moves through a potential difference will be equal to the change in potential multiplied by the charge

ΔVqW It is independent of the path taken.

+

-

60V

In each case the same amount of work has to be done against the electric field

HL

When an electron is accelerated across a potential difference in a vacuum the work done on the electron is turned into kinetic energy, therefore

HL

P 505 Ex 17-1 Electron in TV tube. Suppose an electron in the picture tube of a television set is accelerated from rest through a potential difference of 5000 V (a) What is the change in the potential energy of the electron? (b) What is the speed of the electron as a result of this acceleration? (c) Repeat for a proton that accelerates through a PD of -5000V.

HL

As V=gh and as g decreases as we move away from the earth (spacing between field lines increases) the distance between the equipotentials will increase. V = g h g h for same V

+Q

As V=Ed and as E decreases as we move away from the charge (spacing between field lines increases) the distance between the equipotentials will increase. V = E d E d for same V

HL

+ -

HL

HL

+Q

The potential at a point is defined as the work required to bring one coulomb from zero potential (at infinity in this case) to that point.

r

Using calculus and integration we get

where q is a point charge

HL

VX

X

X

XX

X

rV

1

If r doubled then V x 1/2

r 2r 3r 4r 5r 6r 7r 8rDistance in terms of charges radius

++QQ

If r trebled then V x 1/3

V

-X

X

X

XX

X

rV

1

If r doubled then V x 1/2

r 2r 3r 4r 5r 6r 7r 8r

Distance in terms of charges radius

--QQ

This represents the potential near a negative charge. If V at infinity is taken to be zero, energy must be added to a positive charge to move it to infinity. It has negative potential.

Note : We are generally interested in the potential difference between 2 points.

If r trebled then V x 1/3

Potential V as a function of distance r from a single point charge Q when the charge is (a) positive (b) negative

Electric potential of point charge (V=0 at r=)

HL

P 509 Ex 17-3 Work to force 2 + charges close together. What minimum work is required by an external force to bring a charge of q=3.00 C from a great distance away (take r= ) to a point 0.500 m from a charge Q=20.0 C

HL

P 509 Ex 17-4 Potential above two point charges. Calculate the electric potential above the 2 point charges at point A and B. ( this is the same situation as in Ex 16-8 where we calculated the field at these points)

HL

P 511 Con Ex 17-5: Potential Energies. Consider the 3 pairs of charges (a) Which has positive potential energy? (b) which has the most negative potential? (c) Which requires the most work to separate the charges to infinity? Assume all charges have the same magnitude.