By which relation is the deflection of the coil \(\theta\) 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 \(x\text-y\) plane, its path abruptly changes due to the presence of electric and/or magnetic fields beyond \(P\). The curved path is depicted in the \(x\text-y\) plane and is discovered to be noncircular. Which of the following combinations is true?
          
1. \(\vec{{E}}=0 ; \vec{{B}}={b} \hat{i}+{c} \hat{k}\) 
2. \(\vec{E}={a\hat{i}} ; \vec{B}={c} \hat{k}+a\hat{i}\)
3. \(\vec{E}=0 ; \vec{B}=c \hat{j}+b \hat{k}\)
4. \(\vec{E}=a\hat i ; \vec{B}=c\hat{k}+{b}\hat{j}\)

Figure shows the cross-sectional view of the partially hollow cylindrical conductor with inner radius 'R' and outer radius '2R' carrying uniformly distributed current along it's axis. The magnetic induction at point 'P' at a distance $\frac{3R}{2}$ from the axis of the cylinder will be:

1. Zero                               

2. $\frac{5{\mu }_{0}i}{72\mathrm{\pi R}}$

3. $\frac{7{\mu }_{0}i}{18\mathrm{\pi R}}$                             

4.  $\frac{5{\mu }_{o}i}{36\mathrm{\pi R}}$