Question

An insulating solid sphere of radius R is charged in
a non-uniform manner such that volume charge
A
density p=-, where A is positive constant and r
r
is the distance from the center. Electric field at any
inside point a.....​

Answer 1

A/2ε_{0}

Explanation:

Given,

R = radius of the insulating solid sphere

p = A/r (volume charge density)

where,

A = constant

r = distance from the center

$r_{1}$ = distance from any inside point

As we know,

V = 4πr^2

where,

V = volume of spherical solid

With a distance r, 'dr' would be examined as the elemental shell;

∵ dV = 4πr^2

In the shell, the small charge would be;

dq = 4πA.r.dr.

Using integration, we get;

= 2πA.$r_{1^{2} }$

By employing law of Gauss,

Q/ε_{0}  = 4π$r_{1^{2} }$ E

Thus, E(Electric Field strength) = A/ε_{0}

∵ Option 4 is the correct answer.

Learn more: Electric Field Strength

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