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:
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. \(0.96~\text{N-m}\)
Closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, the magnitude of B inside the solenoid near its centre is:
1.\(3.7 \times 10^{-2} \ T\)
2.\(3.1 \times 10^{-2} \ T\)
3.\(2.5 \times 10^{-2} \ T\)
4.\(1.44 \times 10^{-2} \ T\)
Two long and parallel straight wires A and B carrying currents of \(8.0\) A and \(5.0\) A in the same direction are separated by a distance of \(4.0\) cm. The force on a \(10\) cm section of wire A is:
1. | \(3\times10^{-5}\) N | 2. | \(2\times10^{-5}\) N |
3. | \(3\times10^{-4}\) N | 4. | \(2\times10^{-4}\) N |