Question

The field potential inside a charged ball of radius R and centre at o depends only on distance from its center as $V\left(r\right)=\alpha r^2+\beta$ when $\alpha ,\beta$ are +ve constant. now choose correct options

• A. electric field inside the ball $E_r=-2\alpha r$
• B. electric flux passing through an imaginary sphere of radius r centre at O will be $-2\pi \alpha r^4$
• C. volume charge density p(r) inside ball is $-6{\epsilon }_0\alpha$
• D. electric energy of charged ball will be $\frac{48}{5}\pi {\epsilon }_0{\alpha }^2{R}^5$

Answer 1

The correct option is A electric field inside the ball $E_r=-2\alpha r$

Radius $=R$

$V\left(r\right)={ar}^2+\beta$ when,

$\alpha$ and $\beta$ are $(+Ve)$ constant electric field inside the ball $F_r=-2ar$

because,

$-\frac{d{v}_r}{dr}=+2\alpha r=E_r$

or, $E_r=-2\alpha r$ (derivative with respect to $r$)