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

1. $\frac{{\mu }_0}{2\mathrm{\pi r}}{i}_1{i}_{2}dl<mspace\; width="1em"></mspace>\tan \theta$                              2. $\frac{{\mu }_0}{2\mathrm{\pi r}}{i}_1{i}_{2}dl<mspace\; width="1em"></mspace>\sin \theta$

3. $\frac{{\mu }_0}{2\mathrm{\pi r}}{i}_1{i}_{2}dl<mspace\; width="1em"></mspace>\cos \theta$                              4. $\frac{{\mu }_0}{4\mathrm{\pi r}}{i}_1{i}_{2}dl<mspace\; width="1em"></mspace>\sin \theta$

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 $2\mathrm{\pi }\times {10}^{-5}\mathrm{N}/\mathrm{m}$

\(A,B, ~\text{and}~C\) are parallel conductors of equal length carrying currents \(I, I,~\text{and}~2I\) respectively. The distance between \(A\) and \(B\) is \(x\). The distance between \(B~\text{and}~C\) 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 

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