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.\(2.01 \times 10^{-4} \ T\)
 

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: 

 

A square coil of side \(10~\text{cm}\) consists of \(20~\text{turns}\) and carries a current of \(12~\text{A}\). The coil is suspended vertically and the normal to the plane of the coil makes an angle of \(30^{\circ}\) with the direction of a uniform horizontal magnetic field of magnitude \(0.80~\text{T}\). What is the magnitude of torque experienced by the coil?
1. \(0.79~\text{N-m}\)
2. \(0.88~\text{N-m}\)
3. \(0.49~\text{N-m}\)
4. \(0.96~\text{N-m}\)