Problem 1 (25 points) - Solutions
Problem 2 (25 points) - Solutions
The long, straight wire AB shown in the figure carries a current of I1 = 14.0 A. The rectangular loop
whose long edges are parallel to the wire carries a current of I2 = 5.00 A.
(a) (15 pts) Find the magnitude and direction of the net force exerted on the loop by the magnetic
field created by the wire.
(b) (10 pts) Find the magnitude and direction of the force exerted on the wire by the magnetic field
created by the rectangular loop.
I1 =
14.0 A
I2 =
5.00 A
y
x
28.62: (a) The forces on the top and bottom segments cancel, leaving the left and right sides:
→
→
→
⎛ µI
µI ⎞
µ IlI ⎛ 1 1 ⎞
F = F l + F r = −( IlBl )iˆ + ( IlBr )iˆ = Il ⎜⎜ − 0 wire + 0 wire ⎟⎟ iˆ = 0 wire ⎜⎜ − ⎟⎟ iˆ
2πrr ⎠
2π ⎝ rr rl ⎠
⎝ 2πrl
→
⎞ˆ
µ (5.00 A)(0.200 m)(14.0 A) ⎛
1
1
⎜⎜
⎟⎟ i = −(7.97 × 10− 5 N )iˆ.
⇒F = 0
−
2π
⎝ 0.100 m 0.026 m ⎠
28.62: (b) The force on the loop obtained in (a) should have the same magnitude as the force on the wire,
but in an opposite direction:
→
⇒ F = + (7.97 × 10 − 5 N )î .
Problem 3 (25 points) - Solutions
A 1.50-m long metal bar is pulled to the right at a steady 5.0 m/s perpendicular to a uniform 0.750 T
magnetic field. The bar rides on parallel metal rails connected through 25.0 Ω resistor, as shown
in the figure, so the apparatus makes a complete circuit. You can ignore the resistance of the bar and
the rails.
a) (10 pts) Calculate the magnitude of the electromotive force (emf) induced in the circuit.
b) (10 pts) Find the direction of the current induced in the circuit.
c) (5 pts) Calculate the current through the resistor.
29.20:
a) ε = vBl = (5.0 m s)(0.750 T)(1.50 m) = 5.6 V
b) The flux through the circuit is increasing, so the induced current must cause a magnetic field out
of the paper to oppose this increase. Hence this current must flow in a counterclockwise sense.
c) ε = Ri
ε 5 .6 V
i= =
= 0.22 A
R 25 Ω
Problem 4 (25 points) - Solutions
In one form of Tesla coil, a long solenoid with length L and cross-sectional area A is closely wound
with N1 turns of wire. A coil with N2 turns surrounds it at its center.
(a) (10 pts) Find the mutual inductance.
(b) (15 pts) Suppose the current i2 in the outer, surrounding coil is given by i2 = (2.0 x 106 A/s) t. At
time t = 3.0 µs, what average magnetic flux through each turn of the solenoid is caused by the
current in the outer, surrounding coil? What is the induced emf in the solenoid?
L
L = 0.50 m
A = 10 cm2 = 1.0 x 10-3 m2
N1 = 1000 turns
N2 = 10 turns
See Example 30.1 and 30.2 on p.1150-51
or see the next page.
(a)
(b)