Q22 of 44 Page 202

A monoenergetic (18 keV) electron beam initially in the horizontal direction is subjected to a horizontal magnetic field of 0.04 G normal to the initial direction. Estimate the up or down deflection of the beam over a distance of 30 cm (me = 9.11 × 10–31 kg). [Note: Data in this exercise are so chosen that the answer will give you an idea of the effect of earth’s magnetic field on the motion of the electron beam from the electron gun to the screen in a TV set.]

Energy of the electron beam(E) = 18keV = 18000eV = 18000 × 1.6 × 10-19 = 2.88 × 10-15J


Mass of electron (me) = 9.11 × 10–31 kg


Horizontal magnetic field (B) = 0.04 G = 0.04 × 10-4T


Distance of deflection from the beam (r) = 30 cm = 0.3m


Let velocity of electrons be v.


∴ Energy of the beam = Kinetic energy of electrons


⇒ E = 1/2 mev2


⇒


⇒


∴ v = 7.95 × 107m/s


∵ The electron beam deflects along a circular path in a magnetic field.


Let the radius of the circular path be r m.


The force due to magnetic field on the electron = qvBsinθ = e × v × B × sin 90°


Here, q = charge on the electron,


θ = angle between velocity and magnetic field.


∵ The force due to magnetic field on electron = centripetal force on electron


⇒


⇒


⇒


⇒ r = 11.3 m


Let the deflection of electron beam in upward and downward directions be x = r(1-cosΦ),


where Φ = angle of deflection.


∵


⇒ = 0.026


⇒ Φ = sin-1(0.026) = 1.521°


Thus, Deflection(x) = r(1- cosΦ) = 11.3 × (1- cos(1.521)°)


= 11.3 × (1- 0.90)


= 11.3 × 0.01


= 1.1310-3m


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20

A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12 cm. The coil is in a vertical plane making an angle of 45° with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west to east.

(a) Determine the horizontal component of the earth’s magnetic field at the location.


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 21

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60°, and one of the fields has a magnitude of 1.2 × 10–2 T. If the dipole comes to stable equilibrium at an angle of 15° with this field, what is the magnitude of the other field?

 23

A sample of paramagnetic salt contains 2.0 × 1024 atomic dipoles each of dipole moment 1.5 × 10–23 J T–1. The sample is placed under a homogeneous magnetic field of 0.64 T, and cooled to a temperature of 4.2 K. The degree of magnetic saturation achieved is equal to 15%. What is the total dipole moment of the sample for a magnetic field of 0.98 T and a temperature of 2.8 K? (Assume Curie’s law)

 24

A Rowland ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800. What is the magnetic field B in the core for a magnetising current of 1.2 A?