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

Wires 1 and 2 carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element dl of wire 2 at a distance of r from wire 1 (as shown in figure) due to the magnetic field of wire 1

(a) $\frac{{\mu }_0}{2\mathrm{\pi r}}{i}_1{i}_{2}dl \tan \theta$                              (b) $\frac{{\mu }_0}{2\mathrm{\pi r}}{i}_1{i}_{2}dl \sin \theta$

(c) $\frac{{\mu }_0}{2\mathrm{\pi r}}{i}_1{i}_{2}dl \cos \theta$                               (d) $\frac{{\mu }_0}{4\mathrm{\pi r}}{i}_1{i}_{2}dl \sin \theta$

Three long, straight and parallel wires carrying currents are arranged as shown in the figure. The wire C which carries a current of 5.0 amp is so placed that it experiences no force. The distance of wire C from wire D is then 

(1) 9 cm                                         

(2) 7 cm 

(3) 5 cm                                          

(4) 3 cm

A long wire A carries a current of 10 amp. Another long wire B, which is parallel to A and separated by 0.1m from A, carries a current of 5 amp, in the opposite direction to that in A. what is the magnitude and nature of the force experienced per unit length of B $({\mu }_0=4\mathrm{\pi }\times {10}^{-7}weber/amp-\mathrm{m})$

1. repulsive force of ${10}^{-4}N/m$

2. attractive force of ${10}^{-4}N/m$

3. repulsive force of $2\mathrm{\pi }\times {10}^{-5}\mathrm{N}/\mathrm{m}$

4. attractive force of $2\mathrm{\pi }\times {10}^{-5}\mathrm{N}/\mathrm{m}$

A, B, and C are parallel conductors of equal length carrying currents I, I, and 2I respectively. Distance between A and B is x. Distance between B and C is also x. $F_1$ is the force exerted by B on A and $F_2$ is the force exerted by C on A choose the correct answer:

1. $F_1=2F_2$                                 

2. $F_2=2F_1$

3. $F_1=F_2$                                   

4. $F_1=-F_2$ 

There long straight wires A, B and C are carrying current as shown figure. Then the resultant force on B is directed 

(1) Towards A

(2) Towards C

(3) Perpendicular to the plane of paper and outward

(4) Perpendicular to the plane of paper and inward

Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a 25 cm length of wire C is

(1) ${10}^{-3}N$

(2) $2.5\times {10}^{-3}N$

(3) Zero

(4) $1.5\times {10}^{-3}N$

An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current I along the same direction as shown in the figure. Magnitude of force per unit length on the middle wire B is given by:

1. $\frac{{\mu }_o{i}^2}{2\mathrm{\pi d}}$

2. $\frac{2{\mu }_0{i}^2}{\mathrm{\pi d}}$

3. $\frac{\sqrt{2}{\mu }_o{i}^2}{\pi d}$

4. $\frac{{\mu }_o{i}^2}{\sqrt{2}\mathrm{\pi d}}$

A current-carrying closed loop in the form of a right-angle isosceles triangle ABC is placed in a uniform magnetic field acting along AB. If the magnetic force on the arm BC is F, the force on the arm AC is:

1. $\mathbf{-}\mathbf{F}$                                               2. $\mathbf{F}$

3. $\sqrt{2}\mathbf{F}$                                             4. $-\sqrt{2}\mathbf{F}$

A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current $I_{\mathit{1}}$ at a distance d from the conductor as shown in figure. The loop will experience 

(1) a net repulsive force away from the conductor 

(2) a net torque acting upward perpendicular to the horizontal plane

(3) a net torque acting downward normal to the horizontal plane

(4) a net attractive force towards the conductor