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Physics 226
Problem Set #8
.
1) A uniform magnetic field of magnitude 0.078 T passes through a circular
area of radius 0.1 m. The magnetic field lines are oriented at an angle of
25° with respect to a line that is normal to the circular area. Calculate the
flux through the surface.
2) Skid is flying his Cessna Citation II twin engine jet. The length of the
wings from tip to tip is 59 m. The jet is flying horizontally at a speed of 220
m/s. The earth’s magnetic field has a vertical component of magnitude 5.0 x
10-6 T. Calculate the induced EMF between the wing tips.
3) A straight wire is partially bent into the shape of a circle as shown below.
The radius of the circle 2.0 cm. A uniform magnetic field of magnitude 0.55
T is directed perpendicular to the plane of the circle. Each end of the wire is
then pulled so that the area of the circle shrinks to zero. This is done during
a time of 0.25 s. Calculate the magnitude of the average induced EMF
between the ends of the wire.
4) A circular loop of wire with a radius of 20 cm is placed in a uniform
magnetic field of 0.2 T. The field is perpendicular to the plane of the loop.
The loop is removed from the field in 0.3 s. Calculate the average induced
EMF in the loop while it is being pulled out of the field.
5) A long, straight wire has a current running
through it. Above the straight wire is a loop
of wire that is moved towards the straight
wire. The loop then passes over the straight
wire and continues downward, away from
the straight wire. See diagram. Determine
the direction (clockwise or
counterclockwise) of the induced current in
the loop as it is (a) moved towards the wire
from above, (b) moved away from
the wire.
6) Find the direction of the induced current through the resistor in the drawing
below (a) at the instant the switch is closed, (b) after the switch has been
closed for several minutes, and (c) at the instant the switch is opened.
7) Skid needs to design a 60 Hz AC generator to run his stage amplifier for his
gig at Lollapalooza. The generator needs to contain a 150-turn coil whose
area per turn is 0.85 m2 while its maximum EMF needs to be 5500 V. What
should be the magnitude of the magnetic field in which the coil rotates?
8) A 300-turn solenoid has a radius of 5 cm and a length of 20 cm. Find the
energy stored in it when the current is 0.5 A.
9) A step-up transformer is designed to have an output voltage of 2200 V
(rms) when the primary is connected across a 110 V (rms) source. (a) If
there are 80 turns on the primary winding, how many turns are required on
the secondary? (b) If a load resistor across the secondary draws a current of
1.5 A, what is the current in the primary, assuming ideal conditions?
ANSWERS:
1) 2.2 mWb
2) 65 mV
3) 2.8 mV
4) 84 mV
7) 0.11 T
8) 5.55 x 10-4 J
9) a) 1600 turns b) 30 A
Physics 226
Problem Set #7
1) Consider a series RC circuit at the left where C =
6 µ F, R = 2 MΩ, and ε = 20 V. You close the
switch at t = 0. Find (a) the time constant for the
circuit, (b) the half-life of the circuit, (c) the current
at t = 0, (d) the voltage across the capacitor at t = 0,
and (e) the voltage across the resistor after a very
long time
.
2) Given the circuit at the right in which
the following values are used: R1 = 5
kΩ, R2 = 10 kΩ, C = 8 µ F, and ε = 20
V. You close the switch at t = 0. Find
(a) the current through R2 at t=0, and (b)
the voltage across R1 after a long time.
3) Given the circuit at the right in which the
following values are used: R1 = 20 kΩ, R2 =
12 kΩ, C = 10 µ F, and ε = 25 V. You
close the switch at t = 0. Find (a) the
current in R1 and R2 at t=0, (b) the voltage
across R1 after a long time. (Careful with
this one.)
.
4) Using the drawings below: (a) Find the direction of the force on a
proton moving through the magnetic field. (b) Repeat with an electron.
5) An alpha particle has a charge of +2e and a mass of 6.64 x 10-27 kg. It
is accelerated from rest through a potential difference of 1.2 x 106 V and then
enters a uniform magnetic field whose strength is 2.2 T. The alpha particle
moves perpendicular to the field. Calculate (a) the speed of the alpha
particle, (b) the magnitude of the magnetic force exerted on it, and (c) the
radius of its circular path.
6) A 50 g horizontal copper rod has a length of 1.0 m. Calculate the
minimum current in the rod so that it will float in a horizontal magnetic field
of 2.0 T.
7) A 0.5 m length of wire is bent to
form a single square loop. The loop has
12 A of current running through it. The
loop is placed in a magnetic field of
0.12 T as shown at the right (side view
of loop). What is the maximum torque
that the loop can experience?
8) Two very long wires, as shown in the
diagram at the right, each carry currents of
8.0 A, however, they flow in opposite
directions. The distance between the two
wires is 0.12 m. Calculate the net magnetic
field at point A, which is 0.03 m to the left
of the left wire, and at point
B
, which is
halfway between the two wires.
9) A mass spectrometer is shown below. A single charged ion is shot through
the velocity selector into the rectangular deflection chamber. The electric
field between the plates of the velocity selector is 950 V/m. The magnetic
field in the velocity selector and the deflection chamber is 0.93 T. Calculate
the radius of the path of the singly charged ion that has a mass 2.18 x 10 -26
kg.
8)
9)
10) An electron moves at a speed of 1.0 x 104 m/s in a circular
path of radius 2 cm inside a solenoid. The magnetic field of the solenoid is
perpendicular to the plane of the electron’s path. Calculate (a) the
strength of the magnetic field inside the solenoid and (b) the current in the
solenoid if it has 25 turns per centimeter.
ANSWERS:
1) a) 12 s, b) 8.32 s, 5) a) 1.08 x 107 m/s 9) 1.49 x 10-4 m
c) 1 x 10-5 A b) 7.6 x 10-12 N 10) a) 2.8 x 10-6 T
2) a) 2 mA, b) 20 V c) 1.02 x 10-1 m b) 0.89 mA
3) a) I1=1.25 mA, I2=0 6) 0.245 A
b) 15.6 V 7) 0.023 Nm
4) a) P-West, E-East 8) a) 4.3 x 10-5 T
b) 5.3 x 10-5 T
ε
C
R
R1 R2
C
ε
ε
R1
R2 C
v v
v v
B
B
B B
(a) (b) (c) (d)
B
F
F
A B
Electric
Field
Velocity Selector
B
