Consider a spherical shell of radius $R$ with a total charge $+ Q$ uniformly spread on its surface (centre of the shell lies at the origin $x=0$ ). Two point charges $+q$ and $-q$ are brought, one after the other from far away and placed at $x=-a / 2$ and $x=+a / 2( < R)$, respectively. Magnitude of the work done in this process is 

  • [KVPY 2014]
  • A

    $(Q+q)^2 / 4 \pi \varepsilon_0 \alpha$

  • B

    zero

  • C

    $q^2 / 4 \pi \varepsilon_0 a$

  • D

    $Q q / 4 \pi \varepsilon_0 a$

Similar Questions

A particle of mass $m$ and charge $q$ is placed at rest in a uniform electric field $E$ and then released. The kinetic energy attained by the particle after moving a distance $y$ is

  • [AIPMT 1998]

A proton and an anti-proton come close to each other in vacuum such that the distance between them is $10 \,cm$. Consider the potential energy to be zero at infinity. The velocity at this distance will be ........... $\,m / s$

  • [KVPY 2020]

There exists an electric field of magnitude $E$ in $x$-direction. If the work done in moving a charge of $0.2 \,C$ through a distance of $2 \,m$ along a line making an angle $60^{\circ}$ with $x$-axis is $4 \,J$, then the value of $E$ is ........ $N / C$

In a region of space, suppose there exists a uniform electric field $\vec{E}=10 i\left(\frac{ v }{ m }\right)$. If a positive charge moves with a velocity $\vec{v}=-2 \hat{j}$, its potential energy

A unit positive point charge of mass $m$ is projected with a velocity $V$ inside the tunnel as shown. The tunnel has been made inside a uniformly charged non conducting sphere. The minimum velocity with which the point charge should be projected such it can it reach the opposite end of the tunnel, is equal to