Revision/ Ch5/ Q4
Q1
A conducting
circular loop of radius 0.250 m is placed in the xy-plane in a uniform magnetic
field of 0.360 T that points in the positive z-direction, the same direction as
the normal to the plane.
(a)
Calculate the magnetic flux through the loop.
(b)
Suppose the loop is rotated clockwise around the x-axis, so
the normal direction now
points at a 45.0° angle with respect to the z-axis.
Recalculate the magnetic flux through the
loop.
(c)
What is the change in flux due to the rotation of the loop?
[0.0706 Wb, 0.0499 Wb, – 0.0207 Wb]
Q2
A coil with 25
turns of wire is wrapped on a frame with a square cross section 1.80 cm on a
side. Each turn has the same area, equal to that of the frame, and the total
resistance of the coil is 0.350 W. An applied
uniform magnetic field is perpendicular to the plane of the coil, as in figure below.
(a)
If the field changes uniformly from 0.00 T to 0.500 T in 0.800
s, what is the induced emf in the coil while the field is changing?
Find
(b)
the magnitude and
(c)
the direction of the induced current in the coil while the
field is changing.
[– 5.06 ´ 10–3 V, 1.45 ´ 10– 2 A]
Q3
An airplane with a
wingspan of 30.0 m flies due north at a location where the downward component
of Earth’s magnetic field is 0.600 3 1024 T. There is also a component pointing
due north that has a magnitude of 0.470 3 1024 T.
(a)
Find the difference in potential between the wingtips when the
speed of the plane is
2.50 ´ 102 m/s.
(b)
Which wingtip is positive?
[0.450 V, West]
Q4
(a)
The sliding bar has a length of 0.500 m and
moves at 2.00 m/s in a magnetic field of magnitude 0.250 T. Using the concept
of motional emf, find the induced voltage in the moving rod.
(b)
If the resistance in the circuit is 0.500 V, find the current
in the circuit and the power delivered to the resistor. (Note: The current in
this case goes counter clockwise around the loop.)
(c)
Calculate the magnetic force on the bar.
(d)
Use the concepts of work and power to calculate the applied
force.
[0.250 V, 0.500 A, 0.125 W, 6.25 ´ 10– 2 N, (–)ve x-direction,
6.25 ´ 10– 2 N]
Q5
An
AC generator consists of eight turns of wire, each having area A = 0.090 0 m2,
with a total resistance of 12.0 W. The coil
rotates in a magnetic field of 0.500 T at a constant frequency of 60.0 Hz, with
axis of rotation perpendicular to the direction of the magnetic field.
(a)
Find the maximum induced emf.
(b)
What is the maximum induced current?
(c)
Determine the induced emf and current as functions of time.
(d)
What maximum torque must be applied to keep the coil turning?
[136 V, 11.3 A, 136 V sin 377t, 11.3 sin
377t, 4.07 Nm]
Q6
(a)
Calculate the inductance of a solenoid containing 300 turns if
the length of the solenoid is 25.0 cm and its cross- sectional area is 4.00 ´ 10– 4 m2.
(b)
Calculate the self-induced emf in the solenoid described in
part (a) if the current in the solenoid decreases at the rate of 50.0 A/s.
[0.181 mH, 9.05 mV]
