MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Electrostatics Formulae Page 1

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1. Gauss's Theorem:

 The total normal electric induction (TNEI) over a closed surface is equal to the algebraic sum of the electric charges enclosed by the surface. T.N.E.I. =S Q1 T.N.E.I. = K e0 Normal component of ´ surface area K = dielectrict constant of the medium e0 = Permitivitty of free space

2. Electric intensity at a point due to a charged sphere:

E =

 q 4pk Î0 r2

Or

E =

 s R2 k Î0 r2

=

 s kÎ0

(

 R r

)

2

 where q : Total charge on the sphere R : radius of the spherical conductor r : distance of the point from the centre of the sphere s : surface density of charge or the sphere k : dielectric constant of the medium surrounding the sphere.

Remember:
E =0 inside the charged sphere.

E =

 s kÎ0

When point is very close to charged sphere

3. Electric intensity at a point just outside a long cylinder:

E =

 q 2pk Î0 r

Or

E =

 s R k Î0 r

where,

 q : charge per unit length of cylindrical conductor R : radius of cross-section of cylindrical conductor r : distance of point from axis of cylinder s : surface density of charge on cylinder k : dielectric constant of the medium surrounding the cylinder.

4. Electric intensity at a point just outside a closed charged conductor:

E =

 s k Î0

where
s : surface density of charge on the conductor.

5. Mechanical force per unit surface area of a charged conductor:

 F ds

=

 s2 2 Î

=

 s2 2k Î0

=

 1 2

kÎ0 E2

 where E = magnitude of electric intensity at a point just outside the element. k = dielectric constant of the medium surrounding the conductor. s = surface density of charge on the conductor.

6. Energy density of a medium:

Energy per unit volume or Energy density of a medium in which electric field is present

dw =

 1 2

Î0k E2

=

 1 2

 s2 ke0

where,

 k : dielectric constant of the medium E : magnitude of electric intensity in the region s = surface density of charge

7. Capacity of a conductor:

The capacity of a conductor is defined as the ratio of the charge on the conductor to the potential of the conductor

Capacity (C) =

 Charge(Q) Potential(V)

C =

 Q V

\ Q = CV

 1 Coulomb 1 Volt

1 Pico farad (pF) = 10

8. Capacity of a parallel plate condenser:

Capacity of a parallel plate condenser with a medium of dielectric constant k,

C =

 AÎo k d

Cair =

 AÎo d

 where A : area of each plate d : distance between the plates,

C = k Cair

9. Energy stored in a charged condenser:

U =

 Q2 2C

=

 1 2

CV2

=

 1 2

QV

 where Q : magnitude of charge on each plate C : capacity of the condenser V : potential difference between the plates.

10. Equivalent capacity of number of condensers connected in series:

The equivalent capacity of a number of condensers (having capacities C1, C2, …, Cn) connected in series

 1 C

=

 1 C1

+

 1 C2

+...+

 1 Cn

or

 1 C

=

11. Equivalent capacity of number of condensers connected in Parallel:

The equivalent capacity of a number of condensers (having capacities C1, C2, …, Cn) connected in parallel

 C = C1 + C2 + … + Cn or C =

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