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Question

For the given graph between electric field (E) and distance (r) from axis of the infinite uniformly charged hollow cylinder, the outer radius of hollow cylinder is


A
2 m
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B
1 m
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C
1.5 m
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D
0.5 m
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Solution

The correct option is B 1 m
Given that,
r= Distance from axis of cylinder
Let the radius of the cylinder is R and Er is the electric field at distance r from the axis of the cylinder.
Case I: When r>R
Er>R=σRϵ0r
(σ=Surface charge density)

Case II: When r=R
Er=R=σRϵ0r=σϵ0

Case III: When r<R
Er<R=0

For any infinite uniformly charged hollow cylinder, the electric field in the region inside the cylinder is zero and at points just outside the cylinder is maximum and it decreases as distance from the axis increases.
From graph, we can see that at r=1 m, electric field is maximum. Thus, the radius of infinite uniformly charged hollow cylinder is R=1 m.

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