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

A small coil of N turns has an effective area A and carries a current I. It is suspended in a horizontal magnetic field $\stackrel{.}{B}$ such that its plane is perpendicular to $\stackrel{.}{B}$. The work done in rotating it by $180°$ about the vertical axis is 

(a) $NAIB$                               (b) $2NAIB$ 

(c) $2\mathrm{\pi NAIB}$                          (d) $4\mathrm{\pi }NAIB$

Which among the following options needs to be decreased to increase the sensitivity of a moving coil galvanometer?

An electron, moving in a uniform magnetic field of induction of intensity $\stackrel{\rightharpoonup }{B,}$ has its radius directly proportional to :

(1) Its charge                       

(2) Magnetic field

(3) Speed                               

(4) None of these

A particle of charge q and mass m is moving along the x-axis with a velocity of v and enters a region of electric field E and magnetic field B as shown in the figure below. For which figure is the net force on the charge zero?

1.		2.
3.		4.

 A long straight wire along the z-axis carries a current I in the negative z-direction. The magnetic field vector $\overrightarrow{\mathrm{B}}$ at a point having coordinates (x, y) in the z = 0 plane is :

1. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{y}\hat{\mathrm{i}}-\mathrm{x}\hat{\mathrm{j}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$                 

2. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{x}\hat{\mathrm{i}}+\mathrm{y}\hat{\mathrm{j}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$

3. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{x}\hat{\mathrm{j}}-\mathrm{y}\hat{\mathrm{i}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$                 

4. $\frac{{\mathrm{\mu }}_0\mathrm{I}(\mathrm{x}\hat{\mathrm{i}}-\mathrm{y}\hat{\mathrm{j}})}{2\mathrm{\pi }({\mathrm{x}}^2+{\mathrm{y}}^2)}$

Figure shows a square loop ABCD with edge length a. The resistance of the wire ABC is r

and that of ADC is 2r. The value of magnetic field at the centre of the loop assuming

uniform wire is

1. $\frac{\sqrt{2}{\mu }_{0}i}{3\mathrm{\pi a}}\odot$                                 

2. $\frac{\sqrt{2}{\mu }_{0}i}{3\mathrm{\pi a}}\otimes$

3. $\frac{\sqrt{2}{\mu }_{0}i}{\mathrm{\pi a}}\odot$                                   

4. $\frac{\sqrt{2}{\mu }_{0}i}{\mathrm{\pi a}}\otimes$   

A particle with charge q, moving with a momentum p, enters a uniform magnetic field normally. The magnetic field has magnitude B and is confined to a region of width d, where $d<\frac{p}{Bq}$. The particle is deflected by an angle $\theta$ in crossing the field, then:

The unit vectors $\hat{i}, \hat{j} and \hat{k}$ are as shown below. What will be the magnetic field at O in the following figure?

(a) $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{i}{a}\left(2-\frac{\mathrm{\pi }}{2}\right)\hat{j}$             (b) $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{i}{a}\left(2+\frac{\mathrm{\pi }}{2}\right)\hat{j}$

(c) $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{i}{a}\left(2+\frac{\mathrm{\pi }}{2}\right)\hat{i}$              (d) $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{i}{a}\left(2+\frac{\mathrm{\pi }}{2}\right)\hat{k}$ 

A current I is carried by an elastic circular wire of length L. It is placed in a uniform magnetic field B (out of paper) with its plane perpendicular to B's direction. What will happen to the wire?

          \(F ~\)