Physics Formula sheet class 12

ELECTRIC CHARGES AND FIELDS
 Quantization of charge: If n number of electrons are added/removed from a body total
charge q on it is such that

q = ± ne .

 Coulomb’s law
Force between two charges q1 and q2 placed at a distance r in free space is given by

1 q1  q2
Fo = .
4 o r 2

This relation is called Coulomb’s law.

9 Nm
2
1
Value of is 9  10 .
4 o C2

 If there is some medium between the charges, then force is given by

1 q1  q2
Fm = ,
4  r 2

where  is the electrical permittivity of the medium.
 Dielectric constant:

m F
for a medium m dielectric constant is defined as k  , k is also equal to k  o .
o Fm

 Force acting on a charge q placed in an electric field of intensity E is qE. This force is in
the direction of field if charge is positive and in the opposite direction if charge is negative.

1 q
 Electric field at a distance r due to a charge q is E  .
4 o r 2

 Dipole moment = either charge x distance between the charges,

p = q  2a ,

here 2a is the distance between the charges.
 Electric field at any point at a distance r on axial line of an electric dipole

1 2pr
is given by E  ,
4 o (r  a 2 )2
2




1 2p
for short dipole this formula reduces to E  .
4 o r 3

, Electric field at any point at a distance r on equatorial line of an electric dipole is given
1 p
by E  ,
4 o
3

(r  a )
2 2 2




1 p
for short dipole this formula reduces to E  .
4 o r 3

 Torque acting on an electric dipole placed in an electric field is given by

  pE sin  .

 Electric potential energy of a dipole in a uniform electric field is given by
U   pE (cos2  cos1 ) .

 Electric flux through an area is given by

φE =EAcosθ ,

where  is the angle between area vector and electric field vector.
 Gauss theorem. Electric flux through a closed surface containing a charge q is given by

q
φE  .
o

 Electric field intensity at a perpendicular distance r due to a line charge is given by


E ,
2 o r

here  is the linear charge density.
 Electric field at a distance r due to charged spherical shell containing a charge q is

1 q
given by E  .
4 o r 2

1 q
At the surface of the shell field is E  ,
4 o R 2

where R is the radius of the shell.
 Electric field intensity inside a hollow metallic conductor is zero.


 Electric field intensity at a point around a charged sheet is E  ,
o

where  is the surface charge density of the sheet

, ELECTRIC POTENTIAL AND CAPACITANCE
POTENTIAL BASICS

 If a charge qo is brought from infinity to a point in the field of another charge q and the
W
amount of work done is W, then potential at point A is V  .
qo

 When a charge q is taken from a point A to B in an electric field and work done is W, then
W
potential difference between A and B is VAB  VB  VA  .
q

1 q
 Potential at a distance r due to a point charge q is V  .
4πε o r

ELECTRIC DIPOLE

 At a point around electric dipole of dipole moment p, potential at

p
o Axial line is
4πε or 2

o Equatorial line is 0

p cos θ
o At any other point is , where r is the distance of point from centre of dipole
4πε or 2
of and θ is the angle between the dipole axis and line joining the centre of dipole
and point.

dV
 Potential gradient: E   .
dr

 V   Edr cos θ

POTENTIAL ENERGY

 Potential energy of a system of charges q1 and q2 separated by a distance r is
1 q1  q2
U .
4πε o r

1 q1  q2
 Potential energy is external electric field is U   q1V1  q2 V2
4πε o r

EQUIPOTENIAL SURFACE