A long solenoid of \(50~\text{cm}\) length having \(100\) turns carries a current of \(2.5~\text{A}\). The magnetic field at the centre of the solenoid is: 
\(\big(\mu_0 = 4\pi\times 10^{-7}~\text{TmA}^{-1} \big)\)
1. \(3.4\times 10^{-4}~\text{T}\)
2. \(6.28\times 10^{-5}~\text{T}\)
3. \(3.14\times 10^{-5}~\text{T}\)
4. \(6.28\times 10^{-4}~\text{T}\)

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 monoenergetic electron beam with an electron speed of 5.20 x 10⁶ m/s is subject to a magnetic field of 1.30 x 10^-4 T normal to the beam velocity. What is the radius of the circle traced by the beam, given e/m for electron equals 1.76 x 10¹¹ C kg^-1?

1. 22.7 cm
2. 21.3 cm
3. 20.0 cm
4. 21.9 cm

An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure $\left(~{10}^{-2}<mspace\; width="1em"></mspace>mm<mspace\; width="1em"></mspace>of<mspace\; width="1em"></mspace>Hg\right).$ A magnetic field of $2.83\times {10}^{-4}<mspace\; width="1em"></mspace>T$ curves the path of the electrons in a circular orbit of radius 12.0 cm. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the 'fine beam tube' method. Specific charge ratio (e/m) is:
1. \(1.21 \times 10^{11} \mathrm{C}~ \mathrm{kg}^{-1}\)
2. \(1.73 \times 10^{11} \mathrm{C}~\mathrm{kg}^{-1}\)
3. \(2.53 \times 10^{11} \mathrm{C}~\mathrm{kg}^{-1}\)
4. \(3.02 \times 10^{11} \mathrm{C}~\mathrm{kg}^{-1}\)

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