A wire carrying current i is shaped as shown. Section AB is a quarter circle of radius r. The magnetic field is directed :

                                                      
(a) At an angle $\mathrm{\pi }/4$ to the plane of the paper

(b) Perpendicular to the plane of the paper and directed in to the paper

(c) Along the bisector of the angle ACB towards AB

(d) Along the bisector of the angle ACB away from AB

The earth’s magnetic field at a given point is $0.5\times {10}^{-5}Wb-m^{-2}.$ This field is to be annulled by magnetic induction at the center of a circular conducting loop of radius 5.0cm. The current required to be flown in the loop is nearly :

(1) 0.2 A                  

(2) 0.4A

(3) 4A                      

(4) 40A

A part of a long wire carrying a current i is bent into a circle of radius r as shown in the figure. The net magnetic field at the centre O of the circular loop is

(1) $\frac{{\mu }_{0}i}{4r}$                                

(2) $\frac{{\mu }_{0}i}{2\mathrm{\pi r}}\left(\mathrm{\pi }+1\right)$

(3) $\frac{{\mu }_{0}i}{2r}$                                

(4) $\frac{{\mu }_{0}i}{2\mathrm{\pi r}}\left(\mathrm{\pi }-1\right)$

In the figure, what is the magnetic field at the point O

1. $\frac{{\mu }_{0}I}{4\mathrm{\pi r}}$                                  2. $\frac{{\mu }_{0}I}{4\mathrm{\pi r}}+\frac{{\mu }_{0}I}{2\mathrm{\pi r}}$

3. $\frac{{\mu }_{0}I}{4r}+\frac{{\mu }_{0}I}{4\mathrm{\pi r}}$                        4. $\frac{{\mu }_{0}I}{4r}-\frac{{\mu }_{0}I}{4\mathrm{\pi r}}$

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