Two opposite and equal charges each of magnitude $4 \times 10^{-8} \text{ C}$ form a dipole. Their separation is $2 \times 10^{-2} \text{ cm}$. When this dipole is placed in an external electric field of $4 \times 10^8 \text{ NC}^{-1}$,the value of maximum torque and the work done in rotating it through $180^{\circ}$ respectively will be:

  • A
    $64 \times 10^{-4} \text{ Nm}$ and $64 \times 10^{-4} \text{ J}$
  • B
    $32 \times 10^{-4} \text{ Nm}$ and $32 \times 10^{-4} \text{ J}$
  • C
    $64 \times 10^{-4} \text{ Nm}$ and $32 \times 10^{-4} \text{ J}$
  • D
    $32 \times 10^{-4} \text{ Nm}$ and $64 \times 10^{-4} \text{ J}$

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Two charges $-q$ and $+q$ are located at points $(0,0,-a)$ and $(0,0, a)$ respectively.
$(a)$ What is the electrostatic potential at the points $(0,0, z)$ and $(x, y, 0)$?
$(b)$ Obtain the dependence of potential on the distance $r$ of a point from the origin when $r/a > > 1$.
$(c)$ How much work is done in moving a small test charge from the point $(5,0,0)$ to $(-7,0,0)$ along the $x$-axis? Does the answer change if the path of the test charge between the same points is not along the $x$-axis?

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When the distance between two point charges is increased,the electrostatic potential energy of the system:

An electric dipole with dipole moment $\vec p$ is placed in a uniform electric field $\vec E$. The work done in rotating the dipole by $90^\circ$ from its initial equilibrium position is:

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