A high-voltage dc overhead cable carries a current of 2000 A. One 20 m section of the cable has a mass of 120 kg. This cable section is supported so that it is horizontal, with the current in the direction from west to east. The Earth’s magnetic field in this location is 5.0 × 10 –5 T due north and is horizontal. What is the magnitude of the total force exerted by the support on this section of cable? (gravitational field strength = 10 N kg –1)

Answer:

23) D

F = Bilsine
F = force = ?
B = magnetic field = 5 x 10^-5 T
|= current = 2000 A
| = length = 20 m
sine = angle between current and magnetic field.
Since the direction of current is west to east and magnetic field is due north, angle between
current and magnetic field = 90°
sin90≈ 1
F = Bilsine = 5 x 10^-5 T x 2000 x 20 = 2 N
Weight of wire 120 x 10 = 1200 N
ΣF = 1200-2 = 1198 N