Test/Exams

At a minimum the following should be reviewed:

Gauss's Law - calculation of the magnitude of the electric field caused by continuous distributions of charge starting with Gauss's Law and completing all the steps including evaluation of the integrals.

Ampere's Law - calculation of the magnitude of the magnetic field caused by electric currents starting with Ampere's Law and completing all the steps including evaluation of the integrals.

Faraday's Law and Lenz's Law - calculation of induced voltage and current, including the direction of the induced current.

Calculation of integrals to obtain values of electric field, electric potential, and magnetic field caused by continuous distributions of electric charge and current configurations (includes the Law of Biot and Savart for magnetic fields).

Maxwell's equations - Maxwell's contrubution and significance.

DC circuits - Ohm's Law, Kirchhoff's Rules, power, series-parallel combination circuit analysis.

Series RLC circuits - phasor diagrams, phase angle, current, power factor

Vectors - as used throughout the entire course.

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OLD tests #1, #2, and #3 and the final exam from the Fall 2001 semester

OLD final exams from Fall 2000 and Spring 2001

HOMEWORK SOLUTIONS:

(You may need to download a free copy of Acrobat Reader
to view the files below.)

Chapter 21A Electric Charge and Electric Field
SolnA, SolnB

Chapter 25 Current, Resistance and Electromotive Force
SolnA, SolnB

Chapter 26 Direct Current Circuits
SolnA, SolnB

Chapter 21B Electric Charge and Electric Field
SolnA, SolnB

Chapter 22 Gauss's Law
SolnA, SolnB

Chapter 23 Electric Potential
SolnA, SolnB, Soln C

Chapter 24 Capacitance and Dielectrics
SolnA, SolnB, Soln C

Chapter 27 Magnetic Field and Magnetic Forces
SolnA, SolnB

Chapter 28 Sources of Magnetic Field
SolnA, SolnB, Soln C

Chapter 29 Electromagnetic Induction
SolnA

Chapter 30 Inductance
SolnA

Chapter 31 Alternating Current
SolnA

Chapter 32 Electromagnetic Waves
These solutions are not yet available for viewing.

PHYSICS 51 TEST #1 F01��PRINT your name:�

For each problem:

a) Draw a clear and carefully labeled diagram.
b) Write the necessary equations in terms of variables.
c) Explicitly show all steps in calcu�lations, including units.

(30 Points) A 75 Watt (120 V) light bulb is turned on for three weeks (21 days).

Calculate the resistance of the bulb when operating.
Calculate the current through the bulb.
Calculate the monthly cost of the energy ($0.19/kW hour).

(35 Points) Use branch analysis (as done in the text and in class) to write three simultaneous solve for the current in
each of the three branches.�Be sure to solve for the current
in each of the three branches.�Be sure to label the +/-
sides of all resistors and indicate (and label) the assumed direction of your currents.

Circuit is similar to that shown in Fig. 27-9 in textbook, with all emf's and all resistors given.

(35 Points) Two adjacent corners of a square of side 0.065 m are occupied by electric charges of +4.1 (10)^-6 C and �4.1 (10)^-6 C.� Calculate the force (magnitude and direction) on an electron located at one of the other corners of the square.

�_____________________________________________________________

k = 1/4pE_o = 9 (10)⁺⁹ Nm²/C²;�e_o = 1 / (4p * 9 (10)⁺⁹ Nm²/C²)
r_(alum) = 2.75 (10)^-8m; a(_tungstun) = 4.5 (10)^-3 per deg. C.
m_e = 9.11 (10)^-31 kg;��e = -1.6 (10)^-19 C.

PHYSICS 51 TEST #2 F01

For each problem:

a) Draw a clear and carefully labeled diagram.
b) Write the necessary equations in terms of variables.
c) Explicitly show all steps in calculations, including units.

(10 Points) Take-home exam submitted last Monday.
(30 Points) Three capacitors are in series with a 12 Volt battery. The capacitor values are 2.5 uF, 3.3 uF, and 8.5 uF.� Calculate the charge on each of the three capacitors and the voltage drop across each of the three capacitors.
(30 Points) A solid conducting sphere (radius a = 0.23 m) has a surface charge density σ = -4.52 μC/m² and is sur�rounded by a thin conduct�ing spherical shell (radius b = 0.67 m) with total charge q₁ = +3.00 μC. Use Gauss' law (showing all steps) to find the magni�tude of the elec�tric field (also indicate its direction).
1. in the region between the spheres at r = 0.35 m and
2. in the region outside the spheres at r = 1.00 m.�

(30 Points) An insulating rod of length L = 2.1 meters lies along the positive x-axis with one end at the origin. It has a charge per unit length of l =+7.8 (10)^-9 Coulombs / meter.� Showing all steps and evaluating the integral, calculate the value of the electric potential (direction and magnitude) at the point on the x-axis where x = +8.7 m.

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k = 1/4pE_o = 9 (10)⁺⁹ Nm²/C²;� E_o = 1 / (4p p 9 (10)⁺⁹ Nm²/C²)

��dz / z = ln z;�� dx /(x² + a²)^3/2 = x / a² (x² + a²)^1/2�

PHYSICS 51�� TEST #3�� F01��

For each problem:

a) Draw a carefully labeled coordinate system and/or diagram,
b) Write the necessary equations in terms of variables, and
c) Explicitly show all steps in calculations including units.

(25 Points) In this room a uniform magnetic field with magnitude 120 uT points vertically downward.� An electron moves horizontally with a speed of 3.2 (10)⁺⁷ m/s from north to south. Calculate the magnetic force acting on the electron (magnitude in Newtons and direction N, E, S, W, up, or down).
(35 Points) Seventy-seven turns of insulated copper wire are wrapped around a wooden cylinder of cross-sectional area 2.6 (10)^-3 m². The two ends of the wire are connected together. A uniform magnetic field, which makes an angle of 15^degrees with the cylinder�s axis, decreases at a constant rate of 32 mT/sec.

Calculate the emf induced in the circuit.
In your diagram clearly indicate the direction of the induced current.

(40 Points) A circular loop of radius C = 0.12 m lies in the x-y plane and carries a current of 7.7 amps.� Starting with the law of Biot and Savart calculate the magnetic field (vector) at a point on the z-axis where z = 0.08 m.� The direction of the current is counter-clockwise as seen from the positive Z�axis.

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e_o = 8.85 (10)^-12 C²/Nm²�� u_o = 4p (10)^-7 Tm/A

e = 1.6 (10)^-19 C� �� m_e = 9.11 (10)^-31 kg

��dx /(x² + a²)^3/2 = x / a² (x² + a²)^{1/2��}��dx / x� = ln x

PHYSICS 51�� FINAL EXAM�F2001�

Show a labeled diagram and all work including units.

(10 Points)

For each of Maxwell's four equations write the equation in terms of variables and write its name.
Identify the term added by Maxwell.
What physical phenomenon is predicted by Maxwell's equations?

(10 Points) Calculate the electric field at the 60^deg. vertex of a 30-60-90 degree triangle.� There is an electron at each of the other two vertices of the triangle.� The hypotenuse is 5.5 m long.
(20 Points) Using Ampere's law, calculate the magnitude of the magnetic field at a dis�tance r = 0.0054 m from the axis of a long cylindrical wire of radius a approximately 0.0023 m (Note: r > a). The wire carries a current i_O = 150 mA which is uniformly distributed over the cross section of the wire.� (Hint: 1. draw a closed Amperian line, 2. evaluate the closed vector line integral in Ampere's Law explicitly showing or explaining all steps.)
(20 Points) A circular loop antenna 0.31 meters in radius and 2.7 Ohms in resistance lies in the plane of this page. A uniform magnetic field from a TV broadcast station points out of the page and toward you at an angle of 15^deg. from the normal

At what rate must the magnetic field change with time to have an induced current of 12 mA flowing in the loop?�
State the direction of induced current in the wire (cl / ccl).
How much power is being dissipated in the antenna?

A series RLC circuit...

Calculate the inductive reactance, X_L; the capacitive reactance, X_C; the impedance, Z; the phase angle; and the current amplitude, i_m. Draw the phasor diagram for this circuit labeling V_R, V_L, V_C, phase angle, i_m, and E_m.
If the circuit is changed so that X_L = X_C, write the value of the new impedance and state whether the amplitude of the current is increased or decreased from the original circuit.

6. (20 Points) A thin glass rod, 4.2 m in length, lies along the positive x-axis with one end at the origin (x = 0).� It carries a linear charge density
l = +7.3x (10)^-9 C/m, where x is in meters. Calculate the electric potential at a point along the y-axis where y = 5.7 m. Carefully draw and label your coordinate system.

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k = 1/4πe_o = 9 (10)⁺⁹ Nm²/C²;�� m_o = 4π (10)^-7 Tm/A

� dx/(x² + c²)^{^1/2} = ln [x +(x² + c²)^{^1/2}]; e = 1.6 (10)^-19 C.

� dx/(x² + c²)^3/2 = x / c² (x² + c²)^1/2; ��x^{^n} dx = x^ⁿ⁺¹ /n+1

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