Question

Find the graph between electric field intensity and distance $r$ from the centre, for the given arrangement of concentric spheres. Charge in the inner solid sphere is uniformly distributed in volume.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Step 1. Given data,

Charge in the inner solid sphere is uniformly distributed in volume.

From diagram,

The radius of the inner sphere is $a$,

The radius of the second sphere is $b$,

The radius of the outer sphere is $c$,

Step 2. Finding electric field intensity at different points.

We know, electric field, $E=K\frac{Q}{r^2}$

Where, $E$ is the electric field, $K$ is the electrostatic force constant, $r$ is the distance between two charges, and $Q$ is charge at distance $r$.

If $\overrightarrow{R}$ is the distance between two charges in vector form then,

Therefore, by applying the conditions,

For, $0<r<a$ electric field is given by $E=\frac{KQr}{{\overrightarrow{R}}^3}$

$\Rightarrow$ $E\propto r$

For, $a\le r\le b$ electric field is given by $E=\frac{KQ}{{}^{r^2}}$

$\Rightarrow$ $E\propto \frac{1}{r^2}$

For, $b<r\le c$ electric field is given by $E=\frac{2KQ}{{}^{r^2}}$

$\Rightarrow$ $E\propto \frac{1}{r^2}$

for, $r>c$ electric field is given by $E=\frac{3KQ}{r^2}$

$\Rightarrow$ $E\propto \frac{1}{r^2}$

Therefore, the below graphs exactly matches with the obtained relations, as the first part is directly proportional to $r$ and the remaining three curves are inversely proportional $r$.

Hence, the correct option is (B).