Electricity and Magnetism, McGraw Hill, 1963.
6 Two parallel wires of lengthLcarry currentsI 1 andI 2. They
are separated by a distanceR, and we assumeRis much less than
L, so that our results for long, straight wires are accurate. The goal
of this problem is to compute the magnetic forces acting between
the wires.
(a) Neither wire can make a force onitself. Therefore, our first step
in computing wire 1’s force on wire 2 is to find the magnetic field
made only by wire 1, in the spaceoccupiedby wire 2. Express this
field in terms of the given quantities.√(b) Let’s model the current in wire 2 by pretending that there is
a line charge inside it, possessing density per unit lengthλ 2 and
moving at velocityv 2. Relateλ 2 andv 2 to the currentI 2 , using the
result of problem 5a. Now find the magnetic force wire 1 makes on
wire 2, in terms ofI 1 ,I 2 ,L, andR. .Answer, p. 1065
(c) Show that the units of the answer to part b work out to be
newtons.
7 Suppose a charged particle is moving through a region of
space in which there is an electric field perpendicular to its velocity
vector, and also a magnetic field perpendicular to both the particle’s
velocity vector and the electric field. Show that there will be one
particular velocity at which the particle can be moving that results
in a total force of zero on it; this requires that you analyze both
the magnitudes and the directions of the forces compared to one
another. Relate this velocity to the magnitudes of the electric and
magnetic fields. (Such an arrangement, called a velocity filter, is
one way of determining the speed of an unknown particle.)
8 The following data give the results of two experiments in which
charged particles were released from the same point in space, and
the forces on them were measured:
q 1 = 1μC , v 1 = (1 m/s)xˆ, F 1 = (−1 mN)yˆ
q 2 =− 2 μC , v 2 = (−1 m/s)ˆx, F 2 = (−2 mN)yˆ
The data are insufficient to determine the magnetic field vector;
demonstrate this by giving two different magnetic field vectors, both
of which are consistent with the data.
9 The following data give the results of two experiments in which
charged particles were released from the same point in space, and
the forces on them were measured:
q 1 = 1 nC , v 1 = (1 m/s)ˆz, F 1 = (5 pN)xˆ+ (2 pN)yˆ
q 2 = 1 nC , v 2 = (3 m/s)ˆz, F 2 = (10 pN)ˆx+ (4 pN)yˆ
Is there a nonzero electric field at this point? A nonzero magnetic
field?
10 This problem is a continuation of problem 6. Note that the
answer to problem 6b is given on page 1065.
(a) Interchanging the 1’s and 2’s in the answer to problem 6b, what746 Chapter 11 Electromagnetism