A current-carrying wire is placed in a uniform magnetic field in the shape of the curve \(y= \alpha \sin \left({\pi x \over L}\right),~0 \le x \le2L.\) $$
What will be the force acting on the wire?
                   

1.	\(iBL \over \pi\)	2.	\(iBL \pi\)
3.	\(2iBL \)	4.	zero

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

A particle of charge \(+q\) and mass \(m\) moving under the influence of a uniform electric field \(E\hat i\) and a uniform magnetic field \(\mathrm B\hat k\) follows a trajectory from \(P\) to \(Q\) as shown in the figure. The velocities at \(P\) and \(Q\) are \(v\hat i\) and \(-2v\hat j\) respectively. Which of the following statement(s) is/are correct?

For a positively charged particle moving in a  x-y­ plane initially along the x-axis, there is a sudden change in its path due to the presence of electric and/or magnetic fields beyond P. The curved path is shown in the x-y plane and is found to be non-circular. Which one of the following combinations is possible

1.  $\overrightarrow{\mathrm{E}}=0; \overrightarrow{\mathrm{B}}=\mathrm{b}\hat{\mathrm{i}}+\mathrm{c}\hat{\mathrm{k}}$                 

2.  $\overrightarrow{\mathrm{E}}=\mathrm{a}\hat{\mathrm{i}};\overrightarrow{ \mathrm{B}}=\mathrm{c}\hat{\mathrm{k}}+\mathrm{a}\hat{\mathrm{i}}$

3. $\overrightarrow{\mathrm{E}}=0;\overrightarrow{\mathrm{B}}=\mathrm{c}\hat{\mathrm{j}}+\mathrm{b}\hat{\mathrm{k}}$                   

4.  $\overrightarrow{\mathrm{E}}=\mathrm{a}\hat{\mathrm{i}};\overrightarrow{\mathrm{B}}=\mathrm{c}\hat{\mathrm{k}}+\mathrm{b}\hat{\mathrm{j}}$

A conducting loop carrying a current \(I\) is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will tend to

Two long conductors, separated by a distance d carry current $I_1$ and $I_2$ in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $3d$. The new value of the force between them is-

1. $-2F$                           

2.  $2F/3$

3. $-2F/3$                           

4. $-F/3$

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. $1.5\times {10}^{-3}N$

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 galvanometer of resistance, G is shunted by a resistance S ohm. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is

(1) $\frac{S^{\mathit{2}}}{(S+G)}$                                             

(2) $\frac{SG}{(S+G)}$

(3) $\frac{G^{\mathit{2}}}{(S+G)}$                                             

(4) $\frac{G}{(S+G)}$

${\mathrm{O}}^{++}, {\mathrm{C}}^{+}, {\mathrm{He}}^{++}$ and ${\mathrm{H}}^{+}$ ions are projected on the photographic plate with the same velocity in a mass spectrograph. Which one will strike the farthest?
1. ${\mathrm{O}}^{++}$
2. ${\mathrm{C}}^{+}$
3. ${\mathrm{He}}^{++}$
4. H⁺