Question

A long thin wire is charged such that charge per unit length is +).. The wire is inserted in a hollow sphere of radius 2R.

The maximum electric flux coming out of the sphere is​

Answer 1

Given that,

Charge per unit length = λ

Radius = 2 R

The maximum flux change inside be maximum.

The length of rod is 4R.

We need to calculate the maximum electric flux coming out of the sphere

Using gauss law

$\phi=\dfrac{Q}{\epsilon_{0}}$....(I)

We know that,

The charge density is

$\lambda =\dfrac{Q}{l}$

$Q=\lambda l$

Put the value of Q in equation (I)

$\phi=\dfrac{\lambda\times l}{\epsilon_{0}}$

Put the value of l

$\phi=\dfrac{4R\lambda}{\epsilon_{0}}$

Hence,  the maximum electric flux coming out of the sphere is $\dfrac{4R\lambda}{\epsilon_{0}}$