Q20 of 44 Page 202

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.


(b) The current in the coil is reversed, and the coil is rotated about its vertical axis by an angle of 90° in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.

(a) Number of turns in the coil (n) = 30


Radius of coil (r) = 12cm = 0.12m


Current in the coil (I) = 0.35A


Angle of dip (δ) = 45o


Magnetic fields due to current carrying coils (B) =


where, μ0 = Permeability of free space = 4π × 10-7TmA1


B =


= 5.49 × 10-5 T


∴ Horizontal component of the earth’s magnetic field = B sinδ


= 5.49 × 10-5 T × sin45o


= 5.49 × 10-5 T × 0.707


= 3.88 × 10-5 T


(b) When the current in the coil is reversed, and the coil is rotated about its vertical axis by an angle of 90° in the anticlockwise sense looking from above, then the needle will reverse its original direction (i.e. the needle will point from East to West).


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 19

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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?

 22

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.]