formula-sheet for mid-term test

8/16/2019 Formula-sheet for Mid-term Test

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PC1432: List of Constants and Formulae

Speed of light in a vacuum:

c D 2:998 108 m/s

Magnitude of the charge of an electron:

e D 1:602

10

19

C

Magnitude of vector (cross) product of A

and B :

jA Bj D AB sin

Components of C D A B:C x D AyBz AzBy,C y D AzBx AxBz,C z DAxBy AyBx

Definition of a scalar (dot) product:

A B D AB cos

Coulomb’s constant:

k D 140

D 8:988 109 Nm2/C2

Coulomb’s law:

F D 140

jq1q2jr2

General definition of electric flux:

˚E DZ E cos dA

DZ E? dA D

Z E dA

Electric potential energy of two point

charges:

U D 140

qq0

r

Potential due to a point charge:

V D U q0

D 140

q

r

Electron volt:

1 eV D 1:602 1019 J

Mass of an electron:

me D9:109 1031 kg

Permittivity of the vacuum:

0 D 8:854 1012 C2/Nm2

A vector A in terms of its components:

A D Ax Oi C Ay Oj C Az Ok

Scalar (dot) product in component form:

A B D AxBx C AyBy C AzBz

Electric field definition:

E D F q0

Electric field of a point charge:

E D 140

q

r2Or

Gauss’s law:

˚E DI E dA D Qencl

0

Electric potential energy of q0 in the pres-

ence of q1, q2, q3, : : ::

U D q040

q1

r1C q2r2

C q3r3

C

D q0

40Xi

qi

ri

Potential due to a collection of point

charges:

V D U q0

D 140

Xi

qi

ri

1


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Potential due to a continuous distribution

of charge:

V D 140

Z dq

r

Work done by a conservative force:

W a!b DZ ba

F dl D U a U b

Definition of capacitance:

C D QV ab

Capacitors in series:

1C eq

D 1C 1

C 1C 2

C 1C 3

C

Volume density of electric energy in a

vacuum:

u D 120E

2

Definition of resistivity:

D E

J

Relationship between resistance and

resistivity:

R D LA

Terminal voltage of a source with internal

resistance:

V ab

DE I r

Resistors in series:

Req D R1 CR2 CR3 C

Kirchhoff’s junction rule:Xi

I i D 0

Potential difference expressed as an

integral of E :

V a V b DZ ba

E dl DZ ba

E cos dl

Capacitance of a parallel-plate capacitor

in a vacuum:

C D QV ab

D 0Ad

Capacitors in parallel:

C eq D C 1 C C 2 C C 3 C

Potential energy stored in a capacitor:

U D Q2

2C D 1

2CV

2

D 1

2QV

Expression for current:

I D dQdt D njqjvd A

Expression for current density:

J D I A D njqjvd

Definition of conductivity: D 1

Relationship between voltage, current,

and resistance:

V D IR

Definition of electric power:

P

DVI

Resistors in parallel:1

ReqD 1R1

C 1R2

C 1R3

C

Kirchhoff’s loop rule:Xi

V i D 0

2


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Z 1

.a2 C x2/3=2 dx D x

a2p a2 C x2 C C Z

1p x2 C a2dx D ln

x C

p x2 C a2

C C

Z x.a2 C x2/3=2

dxD

1

p a2 C x2 CC

Z 1p a2 x2

dx D sin1xa

C C

Z 1

a2 C x2 dx D 1

a tan1

xa

C C

Z dx

x D ln.x/ C C

Z xn dx D x

nC1

nC 1 C C

Z sinx dx D cos x C C Z cosx dx D sin x C C

sin2 C cos2 D 1cos 2 D 1 2 sin2

sin. / D sin cos. / D cos

where C is a constant.

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formula-sheet for mid-term test

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