If a wire in the form of a square with a side \(a\) carries a current \(i\), then the magnetic induction at the centre of the square wire will be:
(Magnetic permeability of free space = \(\mu_0)\)

1.	\(\dfrac{\mu _{0}i}{2\pi a}\)	2.	\(\dfrac{\mu _{0}i\sqrt2}{\pi a}\)
3.	\(\dfrac{2\sqrt2\mu _{0}i}{\pi a}\)	4.	\(\dfrac{\mu _{0}i}{\sqrt2\pi a}\)

 

Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describes circular path of radius ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ respectively. The ratio of mass of X to that of Y is :

(a)  ${\left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right)}^{1/2}$                         (b)  $\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}$

(c)  ${\left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right)}^2$                             (d)  $\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$  

A beam of ions with velocity $2\times {10}^5\mathit{ }m\mathit{/}s$ enters normally into a uniform magnetic field of $4\times {10}^{-2}$tesla. If the specific charge of the ion is $5\times {10}^7$ C/kg , then the radius of the circular path described will be :

(a) 0.10 m              (b)  0.16 m

(c)  0.20 m              (d) 0.25 m

If the direction of the initial velocity of the charged particle is perpendicular to the magnetic field, then the orbit will be
                                                                      or
The path executed by a charged particle whose motion is perpendicular to magnetic field is :

(1) A straight line                               

(2) An ellipse

(3) A circle                                         

(4) A helix

A proton and an \(\alpha\text-\)particle enter a uniform magnetic field perpendicularly at the same speed. If a proton takes \(25~\mu\text{s}\) to make \(5\) revolutions, then the periodic time for the \(\alpha\text-\)particle will be:
1. \(50~\mu\text{s}\)
2. \(25~\mu\text{s}\)
3. \(10~\mu\text{s}\)
4. \(5~\mu\text{s}\)

An $\mathrm{\alpha }-$ particle travels in a circular path of radius 0.45 m in a magnetic field $\mathrm{B}=1.2 Wb\mathit{/}{m}^{\mathit{2}}$ with a speed of $2.6\times {10}^7 m\mathit{/}sec$ . The period of revolution of the $\mathrm{\alpha }-$ particle is :

(a)  $1.1\times {10}^{-5 }$ sec          (b)  $1.1\times {10}^{-6}$ sec

(c)  $1.1\times {10}^{-7}$ sec           (d)  $1.1\times {10}^{-8}$ sec

A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to the one of the sides of the loop and is in the plane of the loop. If a steady current I is established in wire as shown in figure, the loop will

(1) Rotate about an axis parallel to the wire

(2) Move away from the wire or towards right

(3) Move towards the wire

(4) Remain stationary

Two thin long parallel wires separated by a distance b are carrying a current i amp each. The magnitude of the force per unit length exerted by one wire on the other is

(1) $\frac{{\mu }_0{i}^2}{b^2}$                                 

(2) $\frac{{\mu }_0{i}^2}{2\mathrm{\pi b}}$ 

(3) $\frac{{\mu }_{0}i}{2\mathrm{\pi b}}$                                  

(4) $\frac{{\mu }_{0}i}{2{\mathrm{\pi b}}^2}$ 

To make the field radial in a moving coil galvanometer :

(1) The number of turns in the coil is increased

(2) Magnet is taken in the form of horse-shoe

(3) Poles are cylindrically cut

(4) The coil is wounded on the aluminum frame

In a moving coil galvanometer, the deflection of the coil $\theta$ is related to the electrical current i by the relation

(1) $i\propto \tan \theta$                 

(2) $i\propto \theta$ 

(3) $i\propto {\theta }^2$                    

(4) $i\propto \sqrt{\theta }$