Which of the following graphs correctly represents the variation of magnetic field induction with distance due to a thin wire carrying current?

1.		2.
3.		4.

A circular loop with a radius of 20 cm is placed in a uniform magnetic field B = 2T in the XY plane as shown in the figure. If the loop carries a current of i = 1 A, then the magnitude of torque acting on the loop will be:
       
1.  0.25 N-m

2.  5.2 N-m

3.  2.5 N-m

4.  0.52 N-m

If the planes of two identical concentric coils are perpendicular and the magnetic moment of each coil is \(\mathrm M,\) then the resultant magnetic moment of the two-coil system will be:

When a 12 Ω resistor is connected in parallel with a moving coil galvanometer, its deflection reduces from 50 divisions to 10 divisions. What will be the resistance of the galvanometer?

1. 24 Ω

2. 36 Ω

3. 48 Ω

4. 60 Ω

Which one of the following gives the value of the magnetic field according to Biot-Savart’s law?

What is the magnetic field at point O in the figure?
                    

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

What is a representation of the magnetic field caused by a straight conductor with a uniform cross-section and a steady current of radius 'a'?

1.		2.
3.		4.

A current-carrying wire is placed in a uniform magnetic field in the shape of the curve \(y= \alpha sin ({\pi x \over L}),~0 \underline{<}x \underline{<}~2L\) $$
. What will be the force acting on the wire?
                   

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

1.		2.
3.		4.

A particle of charge +q and mass m moving under the influence of a uniform electric field $\mathrm{E}\hat{\mathrm{i}}$ and a uniform magnetic field  $\mathrm{B}\hat{\mathrm{k}}$ follows a trajectory from P to Q as shown in the figure. The velocities at P and Q are $\mathrm{v}\hat{\mathrm{i}}$ and $-2\mathrm{v}\hat{\mathrm{j}}$ respectively. Which of the following statement(s) is/are correct?