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

Two insulated rings,one of slightly smaller diameter than the other,are suspended along their common diameter as shown. Initially,the planes of the rings are mutually perpendicular. When a steady current is set up in each of them:

Match the following and find the correct pairs.

List-$I$	List-$II$
$(A)$ Fleming's left hand rule	$(i)$ Direction of induced current
$(B)$ Right hand thumb rule	(ii) Magnitude and direction of magnetic induction
$(C)$ Biot-Savart law	(iii) Direction of force due to magnetic induction
$(D)$ Fleming's right hand rule	(iv) Direction of magnetic lines due to current

Answer the following questions:
$(a)$ $A$ magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. $A$ charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
$(b)$ $A$ charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction,and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
$(c)$ An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.

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:

$A$ long,straight wire is turned into a loop of radius $10\,cm$ (see figure). If a current of $8\,A$ is passed through the loop,then the value of the magnetic field and its direction at the centre $C$ of the loop shall be close to