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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 0 r2

 

Or

E =

s R2

k 0 r2

 = 

s

k0

 ( 

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

k0

  When point is very close to charged sphere

 

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

 

E =

q

2pk 0 r

Or

E =

s R

k 0 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 0


where
s : surface density of charge on the conductor.

 

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

 

F

ds

=

s2

2

=

s2

2k 0

=

1

2

k0 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

0k 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 farad =

1 Coulomb

1 Volt


1 micro farad (
mF) = 10-6 farad (F)
1 Pico farad (pF) = 10
-12 farad (F)

 

8. Capacity of a parallel plate condenser:

 

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

C =

Ao k

d

Cair =

Ao

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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