Question

The electric field intensity due to a hollow spherical conductor is maximum

a) outside the sphere

b) on the surface of the sphere

c) at any point inside the sphere

d) only at the centre of the sphere​

Answer 1

The electric field intensity due to a hollow spherical conductor is maximum

• On the SURFACE OF THE SPHERE.

But how to prove?

For any distance r > R (radius of sphere)

$\rm \displaystyle \: \oint E \times ds = \frac{q}{ \epsilon_{0} }$

$\rm \implies \displaystyle \: E \oint ds = \frac{q}{ \epsilon_{0} }$

$\rm \implies \displaystyle \: E = \frac{q}{ 4\pi\epsilon_{0} {r}^{2} }$

$\rm \implies \displaystyle \: E = \frac{kq}{ {r}^{2} }$

Now, for r = R (i.e. on surface of sphere)

$\rm \implies \displaystyle \: E = \frac{kq}{ {R}^{2} }$

And for r < R , after calculation we get;

$\rm \implies \displaystyle \: E = 0$

• This is because no charge is enclosed inside the sphere.

So, we can see that Max Field Intensity is on the surface of the sphere.

• You can also refer to the graph to see the max intensity.