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 ${35}^o$. The magnetic declination is nearly zero. What are the resultant magnetic fields at points 4.0 cm below the cable?

Answer 1

Total magnetic field at the point due to the four wires=$4\times \frac{{\mu }_{0}I}{2\pi r}=0.2G$

By fleming's right hand rule, the direction of above field is North to South.

Horizontal component of earth's magnetic field at this point$=0.39cos{35}^{\circ }G$ from South to North

Thus net horizontal field at this point=$0.39cos{35}^{\circ }G-0.2=0.12G$

Vertical field due to earth at this point=$Bsin{35}^{\circ }=0.22G$

Thus net magnetic field at the point=$\sqrt{{0.12}^2+{0.22}^2}G=0.25G$