Q19 of 44 Page 202

A telephone cable at a place has four long straight horizontal wires carrying a current of 1.0 A in the same direction east to west. The earth’s magnetic field at the place is 0.39 G, and the angle of dip is 35°. The magnetic declination is nearly zero. What are the resultant magnetic fields at points 4.0 cm below the cable?

Current in the wires (I) = 1.0 A (east to west)


The earth’s magnetic field at the place (H) = 0.39G = 0.39 × 10-4T


The angle of dip (δ) = 35°


Magnetic declination (θ) ∼ 0o


Number of wires in the cable (n) = 4


The horizontal component of earth’s magnetic field (H’) = H × cosδ


Magnetic fields due to current carrying cables (B) =


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


The resultant magnetic fields at point 4.0 cm below the cables


R = 4cm = 0.04m


Resultant horizontal magnetic fields (Hh) = H’- B


⇒ Hh = H’- B


⇒ Hh =


⇒ H � �h = (0.39 × 10-4T × cos35o)-


⇒ Hh = 0.39 × 10-4T × 0.819 - 4 × 2 × 25 × 10-7T


⇒ Hh = 0.319 × 10-4T-0.2 × 10-4T


⇒ Hh = 0.119 × 10-4


Or Hh ∼ 0.12 × 10-4 T or 0.12 Gauss


Resultant vertical magnetic field (H � �v �) = vertical component of earth’s magnetic field = H × sinδ


= 0.39 × 10-4T × sin35o


= 0.39 × 10-4T × 0.573


= 0.22 × 10-4T


∴ Resultant magnetic field =



= 0.25 × 10-4T


More from this chapter

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17

Answer the following question:

A certain region of space is to be shielded from magnetic fields. Suggest a method.

 18

A long straight horizontal cable carries a current of 2.5 A in the direction 10° south of west to 10° north of east. The magnetic meridian of the place happens to be 10° west of the geographic meridian. The earth’s magnetic field at the location is 0.33 G, and the angle of dip is zero. Locate the line of neutral points (ignore the thickness of the cable)? (At neutral points, magnetic field due to a current-carrying cable is equal and opposite to the horizontal component of earth’s magnetic field.)

 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.


(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.

 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?