P
Figure 1
i
i
Supplementary Problems for PHYS 241
Test 4
1. An electron moves in a circular path in the magnetic field of an electromagnet. The plane of the electron's
circular path is parallel to the smooth pole faces of the electromagnet. In the region where the electron is
moving the magnetic field is uniform and has magnitude 0.50 T. The electron moves with a speed of
1.5 x 106 m/s.
a. If someone could observe the electron from the north pole of the electromagnet, would the electron move
clockwise or counterclockwise around its circular path?
b. Find the radius of the electron's path to the correct number of significant figures.
2. A straight conducting bar that is parallel to the z-axis is placed in the uniform magnetic field
B = 2.5i + 1.5j T. The length of the bar is 0.80 m.
a. If there is a current of 1.2 A directed upward in the conducting bar find the magnitude and direction of the
force on the bar due to the magnetic field.
b. Find the magnitude and direction of the force on the conducting bar if it is parallel to the x-axis and carries
a current of the 1.2 A in the +x direction.
3. A circular loop of wire lies in the xy-plane. The radius of the loop is 3.4 cm; it carries a current of 0.80 A that
circulates clockwise when viewed from above.
a. Find the magnetic dipole moment of the loop. (Remember that your answer is a vector. Express it in i, j,
k notation.)
b. If the loop is in the uniform magnetic field B = 1.1i T, find the torque on the loop. (Again express your
answer in i, j, k notation.)
4. A semicircular conductor of radius R carries a current i clockwise as shown in Figure 1. Use the Biot-Savart
law to find the magnitude and direction of the magnetic field at point P.
5. A wire of circular cross section carries a current I. In Figure 2 an Amperian loop in the shape of a hexagon is
shown surrounding the wire. The plane of the hexagon is perpendicular to the wire. The length of each side
of the hexagon is 5.0 cm. The magnitude and direction of the magnetic field (due to I) at the center of each
side of the hexagon is given.
a. Approximate the line integral
6
1
by calculating i i
i
B dS B L
C
,
where Li is the length vector of the ith side. (The acute angle each
vector Bi makes with Li is shown in parentheses.)
b. Use Ampere’s law to estimate I. What is the direction of this
current?
C
2.1 T
(12)
2.5 T
(20)
3.0 T
(10)
3.2 T
(0)
3.2 T
(0)
2.9 T
(15)
Figure 2
