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qUESTIONS

In a cyclotron protons are to be accelerated. Radius of its D is 60 cm. and its oscillator frequency is 10 MHz. What will be the kinetic energy of the proton thus accelerated? (Proton mass = 1.67 × 10-27 kg, e = 1.60 × 10-19 C, 1eV = 1.6 × 10-19 J)

A wire loop of the form shown in the figure carries a current I. Obtain the magnitude and direction of the magnetic field at P.

Figure shows a section of a very long cylindrical wire of diameter a, carrying a current I. The current density which is in the direction of the central axis of the wire varies linearly with radial distance r from the axis according to the relation J = J0 r/a. Obtain the magnetic field B inside the wire at a distance r from its centre.

Two long parallel wires going into the plane of the paper are separated by a distance R, and carry a current I each in the same direction. Show that the magnitude of the magnetic field at a point P equidistant from the wires and subtending angle θ from the plane containing the wires, is B = (μ0/π) (I/R)sin 2θ What is the direction of the magnetic field?

A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 10 A in 0.2 s, what is the rate of change of flux linkage with the other coil?

Example :A metal disc is made to spin at 20 revolutions per second about an axis passing through its centre and normal to its plane. The disc has a radius of 30 cm and spins in a uniform magnetic field of0.20 T, which is parallel to the axis of rotation. Calculate(a)The area swept out per second by the radius of the disc,(b) The flux cut per second by a radius of the disc,(c) The induced emf in the disc.

Example 12.1: A coil consists of 400 turns of wire. Each turn is a square of side d = 20cm A uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50 T in 0.8 s, what is the magnitude of induced emf in the coil while the field is changing?

Example 12.2: A long solenoids, as shown in the figure has 200 turns/cm and carries a current i of 1.4 A. The diameter D of the solenoid is 3 cm. A coil C, having 100 turns and a diameter d of 2 cm is kept at the centre of the solenoid. The current in the solenoid is decreased steadily to zero in 20 ms. Calculate the magnitude of emf induced in the coil C when the current in the solenoid is changing.

Example 12.3: A rotating armature of a simple generator consists of a loop ABCD to which connections are made through sliding contacts. The armature is rotated at 1500 rpm in the magnetic field (B) of 0.5 N/ A.m. Determine the induced emf between the terminals P and Q of the generator at the instant shown in the adjoining figure

Example 12.4: A conducting loop of area 1 m² is placed normal to uniform magnetic field 3Wb/m². If the magnetic field is uniformly reduced to 1 Wb/m² in a time of 0.5 s, calculate the induced emf produced in the loop.

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