Problem#1
A surveyor is using a magnetic compass 6.1 m below a power line in which there is a steady current of 100 A. (a) What is the magnetic field at the site of the compass due to the power line? (b) Will this field interfere seriously with the compass reading? The horizontal component of Earth’s magnetic field at the site is 20 μT.Answer:
Known:
a steady current, i = 100 A
The horizontal component of Earth’s magnetic field at the site is B = 20 μT = 2.0 x 10-5 T
(a) the magnetic field at the site of the compass due to the power line is
B = μ0i/2πr
= (4π x 10-7 Wb/A.m)(100 A)/(2π x 6.1 m)
B = 3.3 x 10-6 T = 3.3 μT
(b) Will this field interfere seriously with the compass reading
B/BEarth = 3.3 μT/20 μT = 0.165
This will deflect the compass needle by as much as one degree. However, there is unlikely to be a place on the Earth’s surface where the magnetic field is 20.0 µT. This was likely a typo, and should probably have been 20.0 µT. The deflection would then be some ten degrees, and that is significant.
Problem#2
At a certain location in the Philippines, Earth’s magnetic field of 39 μT is horizontal and directed due north. Suppose the net field is zero exactly 8.0 cm above a long, straight, horizontal wire that carries a constant current. What are the (a) magnitude and (b) direction of the current?
Answer:
Known:
Earth’s magnetic field, B = 39 μT
the magnitude of the current is
B = μ0i/2πr
39 x 10-6 T = (4π x 10-7 Wb/A.m)i/(2π x 8.0 x 10-2 m)
i = 15.6 A
(b) then current be from west to east to produce a field that is directed southward at points below it.
Problem#3
In Fig. 1, two long straight wires are perpendicular to the page and separated by distance d1 = 0.75 cm. Wire 1 carries 6.5 A into the page. What are the (a) magnitude and (b) direction (into or out of the page) of the current in wire 2 if the net magnetic field due to the two currents is zero at point P located at distance d2 = 1.50 cm from wire 2?
 |
| Fig.1 |
Answer:
Wire 2 must have a current flowing out of the page to cancel the field due to wire 1. The condition for the fields due to wire 1 and wire 2 to have the same magnitude is
µoi1/2π(d1 + d2) = µoi2/2πd2
which implies that
i2 = i1d2/(d1 + d2)
i2 = (6.5 A)(1.50 cm)/(0.75 cm + 1.50 cm)
i2 = 4.33 A, out of the page
Problem#4
One long wire lies along an x axis and carries a current of 30 A in the positive x direction. A second long wire is perpendicular to the xy plane, passes through the point (0, 4.0 m, 0), and carries a current of 40 A in the positive z direction. What is the magnitude of the resulting magnetic field at the point (0, 2.0 m, 0)?
Answer:
The contribution to Bnet from the first wire is
B1 = [μ0i1/2πr1]k
B1 = (4π x 10-7 Wb/A.m)(30 A)/(2π x 2.0 m) k = (3.0 x 10-6 T)k
The distance from the second wire to the point where we are evaluating Bnet is r2 = 4 m – 2 m = 2 m,
B2 = [μ0i2/2πr2]i
B1 = (4π x 10-7 Wb/A.m)(40 A)/(2π x 2.0 m) k = (4.0 x 10-6 T)i
and consequently is perpendicular to B1. The magnitude of Bnet is therefore
|Bnet|= [(3.0 x 10-6 T)2 + (4.0 x 10-6 T)2]1/2 = 5.0 x 10-6 T
µoi1/2π(d1 + d2) = µoi2/2πd2
which implies that
i2 = i1d2/(d1 + d2)
i2 = (6.5 A)(1.50 cm)/(0.75 cm + 1.50 cm)
i2 = 4.33 A, out of the page
Problem#4
One long wire lies along an x axis and carries a current of 30 A in the positive x direction. A second long wire is perpendicular to the xy plane, passes through the point (0, 4.0 m, 0), and carries a current of 40 A in the positive z direction. What is the magnitude of the resulting magnetic field at the point (0, 2.0 m, 0)?
Answer:
The contribution to Bnet from the first wire is
B1 = [μ0i1/2πr1]k
B1 = (4π x 10-7 Wb/A.m)(30 A)/(2π x 2.0 m) k = (3.0 x 10-6 T)k
The distance from the second wire to the point where we are evaluating Bnet is r2 = 4 m – 2 m = 2 m,
B2 = [μ0i2/2πr2]i
B1 = (4π x 10-7 Wb/A.m)(40 A)/(2π x 2.0 m) k = (4.0 x 10-6 T)i
and consequently is perpendicular to B1. The magnitude of Bnet is therefore
|Bnet|= [(3.0 x 10-6 T)2 + (4.0 x 10-6 T)2]1/2 = 5.0 x 10-6 T
Post a Comment for "Magnetic Field Due to a Current in a Long Straight Wire Problems and Solutions"