#### Chapters

## Chapter 4 - Moving Charges and Magnetism

#### Pages 169 - 170

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?

A long straight wire carries a current of 35 A. What is the magnitude of the field **B **at a point 20 cm from the wire?

A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of **B **at a point 2.5 m east of the wire.

A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?

What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30º with the direction of a uniform magnetic field of 0.15 T?

A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?

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. Estimate the force on a 10 cm section of wire A.

A 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, estimate the magnitude of **B **inside the solenoid near its centre.

A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the coil makes an angle of 30º with the direction of a uniform horizontal magnetic field of magnitude 0.80 T. What is the magnitude of torque experienced by the coil?

Two moving coil meters, M_{1} and M_{2} have the following particulars:

*R*_{1} = 10 Ω, *N*_{1} = 30,

*A*_{1} = 3.6 × 10^{–3} m^{2}*, **B*_{1} = 0.25 T

*R*_{2} = 14 Ω, *N*_{2} = 42,

*A*_{2} = 1.8 × 10^{–3} m^{2}, *B*_{2} = 0.50 T

(The spring constants are identical for the two meters).

Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M_{2} and M_{1}.

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 × 10^{6} m s^{–1} normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (*e *= 1.6 × 10^{–19} C, *m*_{e}= 9.1×10^{–31} kg)

In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

**a)** A circular coil of 30 turns and radius 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 60º with the normal of the coil. Calculate the magnitude of the counter torque that must be applied to prevent the coil from turning.

**(b)** Would your answer change, if the circular coil in (a) were replaced by a planar coil of some irregular shape that encloses the same area? (All other particulars are also unaltered.)

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. Give the magnitude and direction of the net magnetic field due to the coils at their centre.

A magnetic field of 100 G (1 G = 10^{−4} T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10^{−3} m^{2}. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m^{−1}. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic