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Question

A hollow insulated conducting sphere is given a positive charge of 10μC. What will be the electric field at the centre of the sphere if its radius is 2 metres?
  1. zero
  2. 5μCm2
  3. 20μCm2
  4. 8μCm2

A
zero
B
5μCm2
C
20μCm2
D
8μCm2
Solution
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Step 1: Uniform Charge distribution on outer surface [Refer Figure]

As a property of conductor, Charge will resides on the outer surface of the hollow sphere.
Since the shape of sphere is symmetric, hence charge distribution will be uniform, As shown in the figure.

Step 2: Finding Electric field inside
The given situation is now a uniformly charged hollow conducting shell.
Inside which the Electric field is zero at all points.

Hence correct option is A.

Alternate Solution using Gauss Law:
We can find the electric field inside using Gauss Law as follows:

Consider a gaussian spherical surface of radius r<R
Charge inside gaussian surface qin=0

From gauss theorem:
E.ds =qinε0

At all points of gaussian surface, E is constant radially outwards due to symmetry and ds is perpendicular to the gaussian surface, hence both are parallel and angle between them is zero.

Eds cos0o =Eds =qinε0

Full area of gaussian surface is 4πr2
E×4πr2=1ε0×0
E=0

Hence, option A is correct.

2107848_195748_ans_4f2dc7b1f4c946bcba8422ea5199b720.png

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