Statement $I$ : The electric force changes the speed of the charged particle and hence changes its kinetic energy: whereas the magnetic force does not change the kinetic energy of the charged particle

Statement $II$ : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below

$(a)$ Shape of loop

$(b)$ Area of loop.

$(c)$ Current in loop

$(d)$ External magnetic field.

The magnitude of magnetic field of a dipole $m$, at a point on its axis at distance $r$, is $\frac{\mu_0}{2 \pi} \frac{m}{r^3}$, where $\mu_0$ is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments, $m_1$ and $m_2$, separated by a distance $r$ on the common axis, with their north poles facing each other, is $\frac{k m_1 m_2}{r^4}$, where $k$ is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles.

($1$) When the dipole $m$ is placed at a distance $r$ from the center of the loop (as shown in the figure), the current induced in the loop will be proportional to

$(A)$ $\frac{m}{r^3}$ $(B)$ $\frac{m^2}{r^2}$ $(C)$ $\frac{m}{r^2}$ $(D)$ $\frac{m^2}{r}$

($2$) The work done in bringing the dipole from infinity to a distance $r$ from the center of the loop by the given process is proportional to

$(A)$ $\frac{m}{r^5}$ $(B)$ $\frac{m^2}{r^5}$ $(C)$ $\frac{m^2}{r^6}$ $(D)$ $\frac{m^2}{r^7}$

Give the answer or qution ($1$) and ($2$)