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Zubrzycki: Magnetism 3
Magnetic Force Exerted on a Current Carrying Wire
Magnetic force exerted on a current: The magnitude of the magnetic force FB on W that a
magnetic field B exerts on a current I passing through a wire of length L is
F B on W = ILBsinθ
where θ is the angle between the directions of the B-field and the direction the Length of the wire
points(which is the same direction the conventional current flows). The direction of this
magnetic force is given by the right hand rule for the magnetic force.
3.1 You wonder if instead of supporting your clothesline with two poles you could replace it
with a wire and then support it magnetically by running an electric current through it and using
Earth’s B-field, which near the surface has magnitude 5 x 10-5 T and points north. Assume that
your house is located on the island of Dominica near the equator where the B-field produced by
Earth is approximately parallel to the earth’s surface. The clothesline is 10 m long and with the
hanging clothes has a 2.0 kg mass. What direction should you orient the clothesline and what
electric current is needed to support it? Finally, decide if this seems like a promising way to
support the clothesline—no poles needed! (The wires in homes will only carry currents around
20 A before circuit breakers start to trigger for safety reasons.)
3.2 A 2.0-m long wire has a 10-A current through it. The wire is oriented south to north and
located near the equator. Earth’s B-field has a 4.0 x 10-5 T magnitude in the vicinity of the wire.
What is the magnetic force exerted on the wire?
3.3 An east-west power line at the equator carries 100 A of current toward the east. At this
location Earth's B field has a magnitude of 3.5 x10-5 T and points north. (a) Determine the
magnitude and direction of the magnetic force exerted by Earth’s magnetic field on the 230-m
long 160-kg wire. (b) Compare this force to the gravitational force exerted on the line by Earth.
3.4 Summary: There are significant differences between the force caused by a magnetic field
and the forces caused by gravitational and electric fields. After writing each difference, answer
the question, “How do I know this?”