In a Thomson mass spectrograph,the electric field and magnetic field are applied:

In order to make the parabolas formed by singly ionized ions in one spectrograph and doubly ionized ions in another Thomson's mass spectrograph coincide,the electric fields and magnetic fields are kept in the ratios $1 : 2$ and $3 : 2$ respectively. Then the ratio of the masses of the ions is

Select the dimensional formula of $\frac{B^2}{2\mu_0}$.

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Permeability of free space	$(I) \ [M L^2 T^{-2}]$
$(B)$ Magnetic field	$(II) \ [M T^{-2} A^{-1}]$
$(C)$ Magnetic moment	$(III) \ [M L T^{-2} A^{-2}]$
$(D)$ Torsional constant	$(IV) \ [L^2 A]$

Choose the correct answer from the options given below:

Two circular coils $1$ and $2$ are made from the same wire,but the radius of the first coil is twice that of the second coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?

There exists a uniform magnetic field of magnitude $1\, T$ and a uniform electric field of magnitude $1\, V/m$ along the positive $y-$ axis. $A$ charged particle of mass $1\, kg$ and charge $1\, C$ has an initial velocity of $1\, m/s$ along the $x-$ axis and is at the origin at $t = 0$. Find the coordinates of the particle at time $t = \pi$ seconds.