# Physics 420 Fall 2004 Quiz 1 Wednesday This quiz is worth 6 points. Be sure to show your work and label your final answers.

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1 Quiz 1 Wednesday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. A charge q 1 = +5.0 nc is located on the y-axis, 15 µm above the origin, while another charge q 2 = nc is located on the x-axis, 15 µc to the right of the origin: y q 1 q 2 O x A) Determine the net electric field at the origin due to these two point charges. Express your answer using vector components (x and ŷ). B) An electron is placed at the origin. Determine the force on the electron, again using vector components.

2 Quiz 1 Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. Two identical motionless spheres, each carrying the same charge q, are suspended by strings as shown below: θ θ sphere sphere A) Show that the electrical force on either charge can be expressed using the weight (w) of a sphere through Fe = w tan(θ). B) Suppose θ = 5.0 ο and the spheres are 2.0 cm apart. If the mass of each sphere is 1.0 kg, determine the amount of charge on each sphere.

3 Physics 420 Quiz 2 Wednesday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. Calculate the electric potential 0.50 m from a -3.0 µc point charge. 2. Suppose you moved an electron from infinity (r = ) to r = 0.5 meters away from the -3.0 µc charge. How much work would be required to overcome the electric repulsion?

4 Physics 420 Quiz 2 Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. Two opposite signed point charges are located along the x-axis, as shown below: y a b q -q P x A) Determine the potential at point P, in terms of q, a, and position x ο x ο B) A proton at point P is moved infinitely far away (x ). If a = 1.00 m, q = 2.0 nc, and x ο determine the work required to move the proton.

5 Quiz 3 Wednesday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. A thin rod of length L has a constant line charge density λ = dq/dx, as shown below: x=0 x=d x=d+l A) Determine the electric potential at x = 0. Your solution should be in terms of the variables listed above. B) Show that if D (and D >>L), the potential goes to zero. C) Suppose the rod has a length of 1.0 meter and the total charge on the rod is 1.0 µc. The potential is measured to be 1500 V. Calculate the distance D.

6 Quiz 3 Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. Consider a uniformly charged ring as diagrammed below: y f y y i P x A) Determine the electric potential at point P along the x-axis in terms of x, σ, y i, and y f. B) Suppose y i = 1.0 m and y f = 3.0 m. If the total charge on the ring is 1.0 µc, calculate the potential at x = 0.

7 Quiz 4 Wednesday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. A hollow insulating sphere has a total charge of Q, which is uniformly distributed throughout the volume: Useful information: Volume of spherical shell = (4/3)π(r 3 r i 3 ) Volume charge density ρ = Q/V r i r o A) Using Gauss s Law, determine the electric field when r i < r < r o. B) Determine the electric field outside the sphere (i.e. when r > r o ).

8 Quiz 4 Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. An infinitely-long hollow insulating cylinder has a uniform charge density ρ throughout its volume. The cylinder has an inner radius (r i ) and an outer radius (r ο ) as shown: The volume of a cylindrical solid is wqual to π (r 2 r i 2) L, where L is the length of the section. A) Using Gauss s Law, determine the electric field when r i < r < r ο. r ο r i B) Determine the electric field outside the cylinder (i.e. when r > r ο ).

9 Quiz 5 Wednesday/Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. Examine the capacitor combination below: C 1 = 1.0 F C 2 = 2.0 F C 3 = 5.0 F V = 15 V A) Calculate the equivalent capacitance of this combination. B) Calculate the charge C 1

10 Quiz 6 Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. A 12-Volt battery is connected to a 3.0 Ω resistor. A) A voltmeter across the battery measures 9.0 Volts. Calculate the internal resistance of the battery. B) Calculate the voltage drop across the internal resistance. C) How much power is lost to the internal resistance? Answer using a ratio of power transferred through the internal resistance to power transferred through the 3.0 Ω resistor.

11 Quiz 7 Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. Examine the resistor-capacitor circuit below: R = 50.0 Ω C = 40.0 switch The voltage across the capacitor is initially 10.0V. The switch is closed at t = 0 seconds. A) Determine the voltage across the resistor at t = 0.50 seconds. B) How much charge is on the capacitor at t = 0.50 seconds? C) At what time would the voltage across the capacitor be reduced to 1.00 V?

12 Spring 2004 Quiz 7 Newman s class 1. Consider the circuit shown below with two batteries and 3 resistors: R = 2.0 Ω R = 6.0 Ω R = 3.0 Ω V = 24. V ε =? A) What is the voltage across the 6 Ω Resistor? B) What is the current through the 6 Ω resistor? C) What is the voltage of the unknown battery?

13 Quiz 8 Wednesday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. A 3.0 A current flows around a circular loop, as shown: a B) If the magnetic field at the center of the loop is measured to be 2.0 x 10-4 T, determine the radius of the loop. C) The magnetic field at the center of the loop is pointed out of the paper. In which direction is the current?

14 Quiz 8 Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. A. A proton is projected parallel to an infinitely long wire as shown below: a = 15 cm v = 1200 m/s wire A) A current travels through the wire to produce a magnetic field of 10. µt at the position of the proton. Determine the value of this current. B) The magnetic force on the proton is straight down (towards the wire). In which direction is the current traveling through the wire? Defend your answer! C) Calculate the instantaneous force on the proton.

15 Quiz 9 Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. An infinitely-long cylindrical conductor contains a current density given by the function J = Cr 2, where r is measured from the center axis of the conductor. R A. Determine the magnetic field magnitude inside the conductor (for 0 < r < R) in terms of µ ο, C, and r. B. Suppose the radius of the cylindrical conductor R is 1.0 cm and the coefficient C = 3.0 x 10 9 T/M 4. Determine the magnetic field magnitude 10.0 cm from the center of the wire. (Hint: Note that I = J da ).

16 Quiz 10 Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. An AC generator contains a 100-turn coil which rotates within a uniform magnetic field. Each circular loop has a radius of 0.10 m, and the coil has an angular velocity of 120π rad/s. A) If the peak EMF is 30.0V, determine the strength of the magnetic field. B) Using the fact that the magnetic flux through the coil is maximum at t = 0, determine the EMF when t = 0.50 s.

17 Quiz Extra Credit Thursday This quiz is worth 6 points. Be sure to show your work and label your final answers. 1. The following voltage is applied across a series RLC circuit: v(t) = (60.0 Volts) sin (1000t). The resistance is 600 Ω, the inductance is H, and the capacitance is 2.50 µf. A) Calculate the maximum current passing through this RLC circuit. B) Calculate the phase angle between the applied voltage and the current through the supply. C) At what angular frequency (ώ) would the inductive reactance be 10 times larger than the capacitive reactance?

18 Midterm I Each question is worth 25 points. Be sure to show your work and label your answers. 1. The square plates of an ideal parallel plate capacitor have a length of 2.50 cm and are 5.0 µm apart. A) If 10.0 Volts are applied across the plates, calculate the amount of charge on either plate. B) An electron is ejected from the negative plate. If the electron starts at rest and encounters no resistance, how fast is it traveling when it reaches the opposite plate?

19 Midterm I Each question is worth 25 points. Be sure to show your work and label your answers. 2. Two charged spherical conducting shells are concentric, as shown below: q ο = +Q b a q i = -2Q A. In terms of Q, a, b, and radius r, determine the electric field between the shells (i.e. for a < r < b). B. Using the same variables in part (A), determine the electric potential between the shells (i.e. for a < r < b).

20 Midterm I Each question is worth 25 points. Be sure to show your work and label your answers. 3. A proton is 20.0 cm from a 1.00-m long positively charged rod, which has a uniform linear charge density. Proton Rod (+Q) A) If the net electric force between the rod and the proton is 1.80 x N, determine the linear charge density of the rod (in coulombs per meter). B) How much energy would it take to move the proton from 20.0cm to 10.0cm from the left end of the rod?

21 Midterm I Each question is worth 25 points. Be sure to show your work and label your answers. 4. An 9.00 nc point charge rests 1.00 meters from a nc point charge, as shown below: q 1 = nc q 2 = 8.00 nc d = 1.00 m A) Is the net electric field equal to zero anywhere around these charges? If so, determine where relative to the nc charge. B) In the space below, draw the electric field diagram of these charges.

22 Midterm I Extra Credit Each question is worth 25 points. Be sure to show your work and label your answers. 1. The square plates of an ideal parallel plate capacitor have a length of 7.50 cm and are 2.oo µm apart. -Q +Q x A) If 1.50 Volts are applied across the plates, calculate the amount of charge Q. B) Determine the potential between the plates as a function of x. Set the potential to be zero on the negative plate.

23 Midterm I Extra Credit Each question is worth 25 points. Be sure to show your work and label your answers. 2. Two charged cylindrical conducting shells are concentric, as shown below: σ ο = -3 σ i b a A) In terms of σ i, a, b, and the radius r, determine the electric field between the shells (i.e. for a < r < b). B) Using the same variables in part (A), determine the electric potential between the shells (i.e. for a < r < b).

24 Midterm I Extra Credit Each question is worth 25 points. Be sure to show your work and label your answers. 3. A µc point charge is 20.0 cm from the center of a 1.00-m long positively charged rod, which has a uniform linear charge density: Point Charge Rod x = m x = 0 x = m A) If the net electric force between the rod and the proton is 7.00 x 10-2 N, determine the linear charge density of the rod (in coulombs per meter). B) How much energy would be released if the point charge moved half the distance to the rod?

25 Midterm II Each question is worth 25 points. Be sure to show your work and label your answers. 1. Examine the diagram below: C 3 = 2.0 µf C 1 = 4.0 µf V = 30.0 V C 2 =? A) If the equivalent capacitance of this combination is 1.0 µf, determine C 2. B) How much energy is stored by C 1? C) Suppose C 3 is submerged in silicone oil (κ = 2.5) while the voltage remains connected. What is the new equivalent capacitance?

26 Midterm II Each question is worth 25 points. Be sure to show your work and label your answers. 2. A uniform conductor has a length of 0.20 meters, a cross-sectional area of 3.0 x 10-5 m 2, and a resistivity of 1.0 x 10-2 Ω at 20 ο C: A) At 30 ο C, the resistance is measured to be 33.3Ω. Determine the temperature coefficient of this material. B) At what temperature would the power transfer through the conductor be reduced to half that when the conductor is at 20 ο C?

27 Midterm II Each question is worth 25 points. Be sure to show your work and label your answers. 3. A 6.0-V battery is connected to a 2.0 Ω resistor. A) The terminal voltage is measured to be 4.0V. Calculate the internal resistance. B) Calculate the power through the internal resistance. C) An identical 6.0-V battery is connected in series to the other components, so the terminal voltages add. Does the current through the 2.0 Ω resistor change? If so, calculate the new current.

28 Midterm II Each question is worth 25 points. Be sure to show your work and label your answers. 4. A proton moves through a uniform 0.3 T magnetic field at an angle of 45 ο, as shown below: B q v A) Determine the magnitude and direction of the magnetic force acting on the particle. B) Suppose an electric field is introduced to keep the particle moving in a straight line. Dete3rmine the strength and direction of this electric field.

29 Midterm III Each question is worth 25 points. Be sure to show your work and label your answers. 1. Two currents, I 1 and I 2 run parallel along infinitely-long conductors, as shown below: I 1? I 2 x x = -d x = 0 x = +2d The net magnetic field at the origin (x 0) is equal to µ ο I 2 / 2πd. A) Find the current I1 in terms of I2. B) There are two solutions Find the other solution!

30 Midterm III Each question is worth 25 points. Be sure to show your work and label your answers. 2. A conducting sheet is placed in a 2.3 T magnetic field. When a 60 ma current flows through the plate, a 2.0 µ V Voltage is measured between the top and bottom edge, as shown below: B (into the page) x I x x x x x d = 2.0 cm V - + The (+) and (-) symbols represent higher and lower potentials, respectively. The sheet has a thickness of 5.0 µm. A) Determine the charge density of the conductor, in C/m 3. B) Calculate the drift velocity of the charges through the plate. C) What charge is carrying the current? Negative or positive? Defend your answer!

31 Midterm III Each question is worth 25 points. Be sure to show your work and label your answers. 3. A resistive-inductive (RL) circuit is connected in series to a 20.0V source at exactly t = 0 seconds. The inductor has a value of 100. mh, while the resistor has a value of 20.0 Ω. A) Calculate the time it takes for the voltage across the resistor to be 15.0 V. B) Calculate the energy stored by the inductor at t = 1.00 x 10-2 seconds. C) Show that the time constant L/R has units of seconds.

32 Midterm III Each question is worth 25 points. Be sure to show your work and label your answers. 4. A single conducting loop has a radius of m. A uniform, external magnetic field is parallel to the area vector of the loop, with a magnitude given by: B = α t 2 + δ Where t is time, α = x 10-2 T/S 2, and δ = 1.00 T A) Determine the induced voltage at t = 2.00 seconds. B) Determine the direction of the induced magnetic field. C) The hoop has a resistance of 1.00 Ω. Determine the net magnetic field at the center of the loop at t = 2.00 seconds.

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