In a chamber, a uniform magnetic field of \(6.5 ~\text G~ (1 ~\text G = 10^{–4}~\text  T)\) is maintained. An electron is shot into the field with a speed of \(4.8 × 10 ^6~\text{ms}^{–1}\) normal to the field. the radius of the circular orbit is:
\((\text{take}~e = 1.6 × 10^{–19}~\text  C,  ~𝑚_𝑒  = 9.1×10^{–31}~\text{kg})\)
1. \(4.2~\text{cm}\)
2. \(5.3~\text{cm}\)
3. \(4.7~\text{cm}\)
4. \(5.2~\text{cm}\)

A circular coil of \(30\) turns and a radius of \(8.0 ~\text{cm}\) carrying a current of \(6.0 ~\text{A}\) is suspended vertically in a uniform horizontal magnetic field of magnitude \(1.0 ~\text{T}.\) The field lines make an angle of \(60^\circ\) with the normal of the coil. What will be the magnitude of the counter-torque that must be applied to prevent the coil from turning?
1. \(7.12 ~\text{N-m}\)
2. \(3.13~\text{N-m}\)
3. \(6.50~\text{N-m}\)
4. \(4.44~\text{N-m}\)

Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A, coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. The magnitude and direction of the net magnetic field due to the coils at their centre is:
1. \(2 \pi \times 10^{-4}\text{ T (East)}\)
2. \(5 \pi \times 10^{-4}\text{ T (East)}\)
3. \(5 \pi \times 10^{-4}\text{ T (West)}\)
4. \(4 \pi \times 10^{-4}\text{ T(West)}\)

For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by, \(B=\frac{\mu_0 I R^2 N}{2\left(x^2+R^2\right)^{\frac{3}{2}}}\)

The magnetic field at the centre of the coil is:
1. \(\frac{\mu_0 I N}{R}\)
2. \(\frac{2 \mu_0 I N}{R}\)
3. \(0\)
4. \(\frac{\mu_0 I N}{2 R}\)

A short bar magnet placed with its axis at \(30^{\circ}\) with a uniform external magnetic field of \(0.25~\text{T}\) experiences a torque of magnitude equal to \(4.5\times 10^{-2}~\text{J}.\)$$
 What is the magnitude of the magnetic moment of the magnet?
1. \(0.36~\text{J/T}\)
2. \(0.21~\text{J/T}\)
3. \(0.01~\text{J/T}\)
4. \(0.12~\text{J/T}\)

A closely wound solenoid of \(2000\) turns and area of cross-section as \(1.6\times10^{-4}~\text m^2,\) carrying a current of \(4.0~\text A,\) is suspended through its center allowing it to turn in a horizontal plane. The magnetic moment associated with the solenoid is:
1. \(0.18~\text{Am}^2\)
2. \(3.24~\text{Am}^2\)
3. \(1.28~\text{Am}^2\)
4. \(0.38~\text{Am}^2\)

A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, the magnetic field inside the core of the toroid is:

1. 3×10^-2 T
2. 0
3. 2×10^-3 T
4. 1×10^-2 T

An electron emitted by a heated cathode and accelerated through a potential difference of 2.0 kV, enters a region with a uniform magnetic field of 0.15 T. if the field is transverse to its initial velocity, the radius of the circular path is:

1. 2.10 mm
2. 0.11 mm
3. 1.01 mm
4. 0.12 mm

A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

1.\(3.14 \times 10^{-4} \ T\) 
2.\(2.12 \times 10^{-4} \ T\) 
3.\(1.41 \times 10^{-4} \ T\) 
4.\(2.01 \times 10^{-4} \ T\)
 

Two moving coil meters, M₁ and M₂ have the following particulars: 

R₁ = 10 Ω, N₁ = 30, A₁ = 3.6 x 10^-3 m² and B₁ = 0.25 T

R₂ = 14 Ω, N₂ = 42, A₂ = 1.8 x 10^-3 m² and B₂ = 0.50 T

( The spring constants are identical for the two meters.)
The ratio of current sensitivity (M₂ to M₁) is: