Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describes circular path of radius ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ respectively. The ratio of mass of X to that of Y is :

1.  ${\left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right)}^{1/2}$                        2.  $\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}$

3.  ${\left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right)}^2$                            4.  $\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$  

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

A small coil of N turns has an effective area A and carries a current I. It is suspended in a horizontal magnetic field $\stackrel{.}{B}$ such that its plane is perpendicular to $\stackrel{.}{B}$. The work done in rotating it by $180°$ about the vertical axis is 

1. $NAIB$                               2. $2NAIB$ 

3. $2\mathrm{\pi NAIB}$                           4. $4\mathrm{\pi }NAIB$

Which among the following options needs to be decreased to increase the sensitivity of a moving coil galvanometer?

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

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

A particle with charge \(q\), moving with a momentum \(p\), enters a uniform magnetic field normally. The magnetic field has magnitude \(B\) and is confined to a region of width \(d\), where \(d< \frac{p}{Bq}.\) The particle is deflected by an angle \(\theta\) in crossing the field, then:

 The unit vectors \(\hat{i} ,   \hat{j}   ~\text{and} ~ \hat{k}\) are as shown below. What will be the magnetic field at \(O\) in the following figure?

1. \(\frac{\mu_{0}}{4 \pi} \frac{i}{a} 2 - \frac{\pi}{2} \hat{j}\)             
2. \(\frac{\mu_{0}}{4 \pi} \frac{i}{a}2 + \frac{\pi}{2} \hat{j}\)
3. \(\frac{\mu_{0}}{4 \pi} \frac{i}{a}2 + \frac{\pi}{2} \hat{i}\)             
4. \(\frac{\mu_{0}}{4 \pi} \frac{i}{a} 2 + \frac{\pi}{2} \hat{k}\)