A 30 ma long, 0.50 cm diameter copper cable running east-west carries an electri
ID: 1536967 • Letter: A
Question
A 30 ma long, 0.50 cm diameter copper cable running east-west carries an electric current of 120 A directed west. At the location of the cable, the Earth's magnetic field is 0.50 times 10^-4 T directed northward and down at an angle of 60 degree below the horizontal. (a) What are the magnitude and direction of the magnetic force that acts on the cable due to the Earth's magnetic field? (b) How does this force compare with the cable's weight? Should this force be considered when designing mechanical supports for the cable? [Copper's density is 8.96 times 10^3 kg/m^3.]Explanation / Answer
length of wire, L = 30 m
radius of wire, r = 0.25cm
direction, east to west (-x axis)
Magnetic field of earth, B = 0.5*10^-4 T ( North direction, 60 degree titled below horizontsal)
current in wire, i = 120 A
a) Magnetic force on a current carrying wire = BIL sin(theta)
for the given case theta = 90 degree, ( wire is in west to east and B is from south to north, so perpendicular)
F = BiL = 0.5*10^-4 * 120 * 30 = 0.18 N
b) Volume of wire = A*L = pi*r^2*L = 5.8875*10^-4 m^3
density = 8.96*10^3 kg/m^3
mass = density*volume = 5.2752 kg
weight = mg = 51.74 N
this is very high as compared to the magnetic foece and hence the magnetic force can be somewhat neglected during design
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