Question

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?

Answer 1

The earth’s magnetic field, B = 0.39 G;
δ = 35°
Therefore, horizontal component of the earth’s  magnetic field,

B_H = B cosδ

Or B_H = 0.39 x cos 35°

= 0.39 x 0.819

= 0.3195 G

The vertical component of the earth's magnetic field,

B_V = B sin δ

= 0.39 x sin 35°

= 0.39 x 0.5736

= 0.2239 G

The magnetic field produced by the four wires of the telephone cable,

Resultant field below the cable:
According to the right hand thumb rule, the direction of b’ at a point below the cable will be opposite to B_H.
Therefore, at a point 4 cm above the cable,
B’_H = B_H + B'
0.3195 + 0.2
= 0.5195 G
B_v = 0.2237 G
Therefore, the resultant magnetic field above the cable,