What is a representation of the magnetic field caused by a straight conductor with a uniform cross-section and a steady current of radius \(a\)?

1.		2.
3.		4.

A non-planar loop of conducting wire carrying a current I is placed as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic field due to this loop at the point P (a,0,a) points in the direction

(1)  $\frac{1}{\sqrt{2}}\left(-\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)$                                   

(2) $\frac{1}{\sqrt{3}}(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$

(3)  $\frac{1}{\sqrt{3}}(-\hat{\mathrm{j}}+\hat{\mathrm{k}}+\hat{\mathrm{i}})$                             

(4)  $\frac{1}{\sqrt{2}}(\hat{\mathrm{i}}+\hat{\mathrm{k}})$                        

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

1.		2.
3.		4.

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?
                   

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

The ratio of the magnetic field at the centre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be

(a) $\frac{{\mathrm{\pi }}^2}{4\sqrt{2}}$                             (b) $\frac{{\mathrm{\pi }}^2}{8\sqrt{2}}$

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

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?

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

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