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

By which relation is the deflection of the coil θ related to the electrical current i in a moving coil galvanometer?

1. $i\propto \tan \theta$                 

2. $i\propto \theta$ 

3. $i\propto {\theta }^2$                    

4. $i\propto \sqrt{\theta }$ 

A moving coil galvanometer has N number of turns in a coil of effective area A, it carries a current I. The magnetic field B is radial. The torque acting on the coil is 

(1) $N{A}^2{B}^{2}I$                          

(2) $NAB{I}^2$

(3) $N^{2}ABI$                            

(4) $NABI$

Three long, straight, and parallel wires carrying currents of 30 A, 10 A, and 20 A in P, Q, and R, respectively, are arranged as shown in the figure. What is the force experienced by a 10 cm length of wire Q?

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

(a)  $\frac{1}{\sqrt{2}}\left(-\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)$                                   (c) $\frac{1}{\sqrt{3}}(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$

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

 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 circular coil is in y-z plane with centre at origin. The coil is carrying a constant current. Assuming direction of magnetic field at x = – 25 cm to be positive direction of magnetic field, which of the following graphs shows variation of magnetic field along x-axis

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) $\frac{\mathrm{\pi }}{4\sqrt{2}}$ 

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

(a) $\frac{\sqrt{2}{\mu }_{0}i}{3\mathrm{\pi a}}\odot$                                  (b) $\frac{\sqrt{2}{\mu }_{0}i}{3\mathrm{\pi a}}\otimes$

(c) $\frac{\sqrt{2}{\mu }_{0}i}{\mathrm{\pi a}}\odot$                                   (d) $\frac{\sqrt{2}{\mu }_{0}i}{\mathrm{\pi a}}\otimes$   

When a positively charged particle moves in an x-y plane, its path abruptly changes due to the presence of electric and/or magnetic fields beyond P. The curved path is depicted in the x-y plane and is discovered to be noncircular. Which of the following combinations is true?
          
1. \(\overrightarrow{\mathrm{E}}=0 ; \overrightarrow{\mathrm{B}}=\mathrm{b} \hat{\mathrm{i}}+\mathrm{c} \widehat{\mathrm{k}}\) 
2. \(\overrightarrow{\mathrm{E}}=\mathrm{ai} ; \overrightarrow{\mathrm{B}}=\mathrm{c} \widehat{\mathrm{k}}+\mathrm{a} \hat{\mathrm{i}}\)
3. \(\vec{E}=0 ; \vec{B}=c \hat{j}+b \widehat{k}\)
4. \(\overrightarrow{\mathrm{E}}=\mathrm{ai} ; \overrightarrow{\mathrm{B}}=c \widehat{\mathrm{k}}+\mathrm{b} \hat{\mathrm{j}}\)