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qUESTIONS

An alpha particle (the nucleus of helium atom) (with charge +2e) is accelerated and moves in a vacuum tube with kinetic energy = 10.00 MeV. On applying a transverse a uniform magnetic field of 1.851 T, it follows a circular trajectory of radius 24.60 cm. Obtain the mass of the alpha particle. [charge of electron = 1.62 × 10-19 C]

Example 10.6 Consider a closely wound 1000 turn coil, having radius of l m. If a current of 10A passes through the coil, what will be the magnitude of the magnetic field at the centre?

A circular loop of radius 9.7 cm carries a current 2.3 A. Obtain the magnitude of the magnetic field (a) at the centre of the loop and (b) at a distance of 9.7 cm from the centre of the loop but on the axis

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?

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.

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.

A toroid of narrow radius of 10 cm has 1000 turns of wire. For a magnetic field of 5 × 10⁻² T along its axis, how much current is required to be passed through the wire?

A moving coil galvanometer has been fitted with a rectangular coil having 50 turns and dimensions 5 cm × 3 cm. The radial magnetic field in which the coil is suspended is of 0.05 Wb/m² . The torsional constant of the spring is 1.5 × 10⁻⁹ Nm/ degree. Obtain the current required to be passed through the galvanometer so as to produce a deflection of 30°.

For proton acceleration, a cyclotron is used in which a magnetic field of 1.4 Wb/m² is applied. Find the time period for reversing the electric field between the two Ds.

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