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

please find your answer below

Answer 2

Answer:

Interpreting the problem statement;

Dip angle δ= 35°  

r= 4 cm= 0.04 m  

Earth's Magnetic field R= 0.39*10^−4  

Horizontal component of the magnetic field H= R cosδ  

H =0.39*10^−4 *(cos 35°)

H= 3.19*10^−5 T  

B₁= (4*μ₀*2*I)/ (4π *r) =[(4*10^−7)*(2)*(1)] /0.04 =2*10^−5 T  

The direction of B₁ at Q is vertically inwards to the plane of paper, and the horizontal component of Earth's magnetic field is given by;

H₁= H + B₁  

H₁= (3.19*10^−5) +(2*10^−5 )

H₁= 5.19*10^−5 T

The resultant magnetic field at dip angle;  

R= √(H₁²+V²)  

R= √{(5.19*10^−5)²+(2.2*10^−5)²} T

R = 5.54*10^−5 T  

Hence the resultant magnetic field at point 4 cm above the cable is 5.54*10^−3 T