In a chamber, a uniform magnetic field of 6.5 G (1 G = 10–4 T) is maintained. An electron is shot into the field with a speed of 4.8 × m s–1 normal to the field. the radius of the circular orbit is:
(e = 1.6 × 10–19 C, = 9.1×10–31 kg)
1.4.2 cm
2. 5.3 cm
3. 4.7 cm
4. 5.2 cm
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 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: