Question

The electric field at a distance 2R from the centre
of a charged conducting spherical shell of radius
R is E. The electric field at a distance R/4 from the
centre of the sphere is? ​

Answer 1

Answer:

Let the total charge on the sphere be Q

It is nonconducting dielectric sphere. It is uniformly charged.

So, charge density per volume ρ=

4/3πR

3

Q

=

4πR

3

3Q

.....(1)

Electric field at distance 2R due to the sphere

E=

4πε

1

×

(2R)

2

Q

......(2)

For finding the electric field at a distance

2

R

from the center of sphere, we need to take into account the charge enclosed within the sphere of radius

2

R

only. This obtained from Gauss;s law of flux coming out of a closed spherical surface of radius

2

R

Charge enclosed Q

1

=ρ×Volume

=ρ×

3

4

π(

2

R

)

3

=

6

π

ρR

3

=

6

π

×

4πR

3

3Q

×R

3

=

8

Q

E

1

=

4πε

1

×

(R/2)

2

Q

1

=

4π

1

×

8

Q

×

R

2

4

=

4π

1

×

(2R)

2

Q

=2E

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