A very long straight wire carries a current I. At the instant when a charge +Qat point P has velocity $\overrightarrow{v}$ , as shown, the force on the charge is:

1. Opposite to OX                            
2. Along OX
3. Opposite to OY                             
4. Along OY

An electric field of 1500 V / m and a magnetic field of 0.40 weber / $mete{r}^2$ act on a moving electron. The minimum uniform speed along a straight line the electron could have is

1. $1.6\times {10}^{15}m/s$                         

2. $6\times {10}^{-16}m/s$

3. $3.75\times {10}^{3}m/s$                         

4. $3.75\times {10}^{2}m/s$

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is:

1. $\frac{{\mathrm{\mu }}_0\mathrm{NI}}{\mathrm{b}}$                                  2. $\frac{2{\mathrm{\mu }}_0\mathrm{NI}}{\mathrm{a}}$

3. $\frac{{\mathrm{\mu }}_0\mathrm{NI}}{2(\mathrm{b}-\mathrm{a})}\ln \frac{\mathrm{b}}{\mathrm{a}}$                         4. $\frac{{\mathrm{\mu }}_0{\mathrm{I}}^{\mathrm{N}}}{2(\mathrm{b}-\mathrm{a})}\ln \frac{\mathrm{b}}{\mathrm{a}}$

An electron, moving in a uniform magnetic field of induction of intensity $\stackrel{\rightharpoonup }{B,}$ has its radius directly proportional to :

1. Its charge                       

2. Magnetic field

3. Speed                               

4. None of these

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