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?
Let us first decide the directions which can best represent the situation. Here, BH=Bcosδ =0.39×cos35oG BH=0.32G and BV=Bsinδ=0.39×sin35oG BV=0.22G Telephone cable carry a total current of 4.0A in direction east to west. We want resultant magnetic field 4.0cm below. Bwire=4πμor2I=10−7×4×10−22×4 =2×10−5T=0.2G=0.2G Net magnetic field Bnet=(BH−Bwire)2+BV2 Bnet=(0.12)2+(0.22)2=0.0144+0.0484=0.25G
