Question

The electric field inside a sphere which carries a charge density proportional to the distance from the centre $\rho =\alpha r$($\alpha$ is a constant) is?

• A. $\frac{\alpha r^3}{4c_0}$
• B. $\frac{\alpha r^2}{4c_0}$
• C. $\frac{\alpha r^2}{3c_0}$
• D. none of these

Answer 1

The correct option is C $\frac{\alpha r^2}{3c_0}$

$\oint \overrightarrow{E}.\overrightarrow{ds}=\frac{Q}{{\epsilon }_0}\Rightarrow Q=\int {\rho }_V$

${\rho }_V=\alpha r$ is given where r is radius

$\overrightarrow{E}.4\pi r^2=\frac{{\rho }_V\frac{4}{3}\pi r^3}{{\epsilon }_0}E=\frac{\alpha r^2}{{3\epsilon }_0}$