Download Magnetic Force Exerted on a Current

Buggé: Magnetism 3 Solns
Magnetic Force Exerted on a Current-Carrying Wire (Continued)
3.2 You wonder if you could support your clothesline by running an electric current through it while it
resides in the 5 x 10-5 T magnetic field due to the Earth. We’ll assume that you are in Costa Rica
near the equator, where the field is parallel to the Earth’s surface. The line is to be 10 m long. You
estimate that with the clothes attached, its mass is 2.0 kg. What direction should you orient the line
and what electric current is needed to support the line? Finally, does this seem like a promising way
to support a clothesline? Explain. (The wires in homes will only carry currents around 20 A before
circuit breakers start to trigger for safety reasons.)
Since the Earth’s magnetic field points from geographic south to geographic north, the clothesline must
be oriented from east to west (or west to east) such that the current is perpendicular to the magnetic
field and the magnetic force is exerted up, away from the Earth.
(9.8 m/s2)
(5 x 10-5 T)
39,000 A
3.3 Regular Problem 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?
Zero; the angle between the current and the magnetic field is 0º.
Buggé: Magnetism 3 Solns
3.4 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.
a) Using RHR #2, Current, east; Magnetic field, north; Force is Out of the Page.
F = ILBsinθ
F = (100 A)(230 m) (3.5 x10-5 T) sin (90) = 0.805 N
b) FEarthonLine = mg = (160 kg)(9.8 m/s2) = 1568 N
3.5 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?”
1. The electric field exerts a force on objects with electric charge. The gravitational field exerts a force
on objects with mass (mass can be thought of as a gravitational "charge".) However, every
“magnetic object” that has ever been found has both a north pole and a south pole, but never just
one pole in isolation.
2. The gravitational and electric forces exerted on objects do not depend on the direction of motion of
those objects, whereas the magnetic force exerted does. If the direction of the electric current is
parallel or anti-parallel to the B-field, no magnetic force is exerted on it.
3. Finally, while the forces exerted by the gravitational and the electric fields are always in the
direction of the g- or E-field (or opposite that direction in the case of a negatively charged object),
the force exerted by the magnetic field on a current carrying wire is perpendicular to both the -field
B and the direction of the electric current