Question

A sphere of radius $r$ has electric charge uniformly distributed in its entire volume. At a distance $d$ from the centre inside the sphere $(d<r)$ the electric field intensity is directly proportional to

• A. $\frac{1}{d}$
• B. $\frac{1}{d^2}$
• C. $d$
• D. $d^2$

Answer 1

The correct option is C $d$

Radius of the sphere $=r$.
Volume of the sphere $=\frac{4}{3}\pi r^3$.
Volume charge density $\rho =\frac{Totalcharge}{Volume}$
$\rho =\frac{Q}{\frac{4}{3}\pi r^3}$
Now consider the sphere of radius $d$.
Charge encloses by sphere with radius $d$.
$q=\rho .\frac{4}{3}\pi d^3$
$=\frac{Q{d}^3}{r^3}$
Electric field intensity
$E=K.\frac{q}{d^2}$
$=\frac{KQd}{r^3}$
As total charge and radius $r$ is constant.
$E\alpha d$