**Physics 4B--Exam 1 Sample Problems**

Solution for above exam:

Other Miscellaneous Phyiscs 4B Exam 1 Problems:

Three point charges are placed along the y-axis as shown.

a. Show that the electric field at points along the x-axis is given by

E(x) = (2kq)[x/(a^{2} + x^{2})^{3/2} - 1/x^{2}]

b. Using the binomial expansion, find E(x) for distant points along the
x-axis and thus verify that E(x) is proportinal to 1/x^{4} for
x>>a.

At
the point P shown in the figure, E = 0.

a. Find the ratio Q/q.

b. If q = 9 x 10^{-9} C, find the magnitude and direction of the
force exerted on an electron positioned midway between Q and q.

The figure shown is an imaginary group of points, lines, and surfaces.
There is an electric field in this space whose components (in N/C) are
given by,

E_{x} = O, E_{y} = 3z, E_{z} = 0 where
z is in meters

a. Find the magnitude and direction of the force on an electron located at the corner of the prism marked C.

b. Find the flux through the surface ABCD.

A thin wire with a charge Q uniformly distributed along its length sets
up an electric field in the space around it.

a. What is the direction of the electric field at the point P as shown
in the figure?

b. Find the magnitude of the electric field at the point P.

Four charges are arranged on the corners of four different rectangles
in the situations shown below. Treating each rectangle separately, place
a vector with its tail at the center of each rectangle showing the direction
of the electric field at that point. (no calculations needed)

Two thin charged concentric spherical shells have radii of 10 cm and 15
cm. The charge on the inner sphere is +4.0 x 10^{-8} C and that
on the outer sphere +2.0 x 10^{-8} C. Find the electric field
at a point that is located at

a. r = 12 cm

b. r = 20 cm

**Physics 4B--Exam 2 Sample Problems**
Given the circuit shown below, assume that the switch has been closed for a long time:

a. Find the current through each resistance.(0.5A through 40,10,and 30 ohm resistors, 0 through 5 ohm resistor)

b. Find the energy stored in the capacitor.(1.6 mJ)

c. Compare the rate at which power is being dissipated in the resistances with the rate at which power is being delivered to the circuit by the battery (calculate numbers).(20 W for both)

d. How long did it take to charge the capacitor to 63% of its maximum charge?(40 x 10^{-6}s)

e. How much energy does a 3 C charge lose as it passes through the 30 ohm resistance?(45 J)

Two point charges, Q_{1} = +2 x 10^{-6}C and
Q_{2} = -3 x 10^{-6}C, are situated as shown.

a. Find the electric potential at point A and at point B.(V_{A}= -4.5 kV, V_{B}= -23.4 kV)

b. Find the work needed to move a point charge,

Q_{3} = 5 x 10^{-6}C from point A to point B along the curved path shown by the solid line.(-94.5 mJ)

A certain wire has a resistance of 20 ohms. Another wire, made of the same material, is exactly 20 percent larger than the first (the length and the diameter are 20 percent larger). Find the resistance of the second wire.(16.8 ohms)

A +5 x 10^{-8}C charge is fixed in position at the origin while an electron located on the x-axis 5 m away is released from rest. The electron begins accelerating toward the positive charge. Find the velocity of the electron when it passes by the 2 m mark on the x-axis.(6.89 x 10^{6} m/s)

**Physics 4B--Exam 3 Sample Problems**
A proton experiences the greatest force as it travels at 3.9 x 10^{5} m/s in a magnetic field when it is moving horizontally westward. The force is upward and of magnitude 8.2 x 10^{-13} N. What is the magnitude and direction of the magnetic field?(B = 13.1 T, South)

Four long straight parallel wires located at the corners of a square of side, a, carry equal currents I_{o} perpendicular to the page as shown in the figure. Find the magnitude and direction of B at the center of the square.

[B = 2
m _{0}I/(pa)to the left in the drawing]

A long straight wire carries a current I_{1}. A short

segment of another wire of length L is oriented perpendicular

to the first wire and carries a current I_{2} as shown. Find the

magnetic force exerted on the second wire due to the first wire.

[F = m _{0}I_{1}I_{2}/(2p) ln{(a + L)/a} acting up the page (parallel to I_{1}]

A rectangular loop of wire (resistance = R) sits with its long side parallel to a very
long wire as shown. The long wire carries a current i.

a. Find the magnetic flux throught the loop as a function of the current, i.[ F _{B} = cim _{o} /(2p) ln{(a + L)/a} ]

b. If the current in the wire changes with time as i(t) = 5t^{2},
find the current induced in the loop as a function of time.

[i(t) = 10ctm _{o} /(2p)ln{(a + L)/a} ]

c. Show the direction of the induced current on the drawing. [counterclockwise]

A long solenoid with 100 turns/m and a radius of 2 cm has a current flowing
through it (in the direction shown by the arrow) which is decreasing at
a rate of 0.2 amp/s. A single loop of wire of 4 cm radius is placed with
its center on the axis of the solenoid and its plane perpendicular to
the axis of the solenoid.

a. Find the emf generated in the outer loop of wire. [e = 3.16 x 10^{-8} volts]

b. Show on the diagram the direction of the induced current that flows
in the outer loop. Explain. [same as direction for solenoid current]

A bar magnet is moving toward the sloenoid as shown below.

a. Indicate on the solenoid wire the direction of the induced current. [CCW as seen by an observer sitting on the magnet looking toward the solenoid]

b. Does the solenoid exert an attractive or repulsive force on the magnet?
Explain. [repulsive]

A 7 H inductor in series with a 200 ohm resistance is suddenly connected to a 50 volt battery. At the instant when the current has risen to 85 percent of its steady state value, find

a. the rate at which the current is increasing.

b. the rate at which energy is being stored in the inductor.

c. the total energy stored in the inductor.

In this problem the values used for current and voltage are understood to be the rms values unless otherwise specified. When the source has a frequency of 400 Hz, the capacitor has an impedance of 8 ohms, the inductor has 32 ohms impedance, and the potential difference across the inductor is 12 volts. The resistance is 10 ohms.

a. Make a phasor diagram showing the voltage across each circuit element.

b. Does the current lead or lag the source voltage? By how much?

c. Find the current in the circuit.

d. Find the voltage, V_{ab}.

e. Find the voltage, V_{ad}.

f. Find the voltage, V_{be}.

g. Find the voltage, V_{ae}.

h. What is the resonant frequency of the circuit?

Find the average energy content of a cubic meter of sunlight as it reaches
the top of the earth's atmosphere, where its intensity is 1340 W/m^{2}.

Given the RL circuit shown,

a. What is the current in the circuit a long time after the switch has
been in position A?

b. Now the switch is thrown quickly from A to B. Find the initial voltage across the 1200 ohm resistor.

c. How long does it take for the current in the inductor to fall to 20 ma?

An LC tank circuit oscillates with a frequency of 5 kHz and has an inductor
with L = 0.5mH . The maximum charge on the capacitor is 75 pC. a. Find
the maximum current in the circuit.

b. Find the current when the charge on the capacitor is 50 pC.