In the figure shown, the magnetic induction at the centre of the arc due to the current in portion AB will be

(a) $\frac{{\mathrm{\mu }}_0\mathrm{i}}{\mathrm{r}}$                       (c)  $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{r}}$

(b) $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{r}}$                        (d) Zero

In a current-carrying long solenoid, the field produced does not depend upon:

A neutral point is obtained at the centre of a vertical circular coil carrying current. The angle between the plane of the coil and the magnetic meridian is :

a) 0                           (b) 45°

(c) 60°                       (d) 90°

If the current is flowing in the south direction along a power line, then what will be the direction of the magnetic field above the power line (neglecting the earth's field)?

An electron and a proton with equal momentum enter perpendicularly into a uniform magnetic field, then :

(1) The path of proton shall be more curved than that of electron

(2) The path of proton shall be less curved than that of electron

(3) Both are equally curved

(4) Path of both will be a straight line

Two particles A and B of masses $m_A$ and $m_B$ respectively and having the same type of charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are $v_A$ and $v_B$ respectively, and the trajectories are as shown in the figure. Then

(1) $m_A{v}_A<m_B{v}_B$                              

(2) $m_A{v}_A>m_B{v}_B$

(3) $m_A<m_B and v_A<v_B$                  

(4) $m_A=m_B and v_A=v_B$

An electric current passes through a long straight wire. At a distance 5 cm from the wire, the magnetic field is B. The field at 20 cm from the wire would be :

(1) $\frac{\mathrm{B}}{6}$                   

(2) $\frac{\mathrm{B}}{4}$

(3) $\frac{\mathrm{B}}{3}$                     

(4) $\frac{\mathrm{B}}{2}$ 

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)  $\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$  

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) $4\mathrm{\pi }NAIB$