5.19 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?
5.19 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?
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1 Answer
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5.19 Number of horizontal wires in the telephone cable, n = 4
Current in each wire, I = 1.0 A
The Earth’s magnetic field at a location, H = 0.39 G = 0.39 T
Angle of dip at the location, = 35
Angle of declination, 0
For a point 4.0 cm below the cable, r = 4.0 cm = 0.04 m
The horizontal component of earth’s magnetic field can be written as
= H - B, where
B = Magnetic field at 4 cm due to current I in four wires = 4
= Permeability of free space = 4 T m
Then B = 4 = 2 T = 0.2 T = 0.2 G
= H – B = 0.39 - 0.2 = 0.12 T= 0.12 G
The vertical component of Earth’s magnetic field is given as
= H
...more
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