A circular coil of \(30\) turns and a radius of \(8.0\) cm carrying a current of \(6.0\) A is suspended vertically in a uniform horizontal magnetic field of magnitude \(1.0\) 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. \(7.12\) N-m
2. \(3.13\) N-m
3. \(6.50\) N-m
4. \(4.44\) 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 \(1.6\times10^{-4}\) m², carrying a current of 4.0 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 Am²
2. 3.24 Am²
3. 1.28 Am²
4. 0.38 Am²

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 $\left(~{10}^{-2} mm of Hg\right).$ A magnetic field of $2.83\times {10}^{-4} T$ 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

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.\(2.01 \times 10^{-4} \ T\)