PH205 FINAL EXAM WINTER 1999

1. In the figure, the separation l between the conducting rods is 45.0 cm. The magnetic field, directed into the page, has a magnitude of 1.20 T. The resistance R of the circuit is 5.1 ohms. The sliding wire is pulled to the right at a constant speed v = 3.30 m/s.

  (a) What is the value of the flux penetrating the conducting loop when the wire is 0.75 m from the resistor?

  (b) What is the current in the circuit?

  (c) What is the value of the magnitude of the external force required to maintain the constant velocity of the moving wire?



2. A 1.6 T magnetic field is perpendicular to the plane of a circular loop of wire (loop radius is 22 cm) and into the page as shown. The sides of the loop are then pushed together at a constant rate to form an elongated loop of zero area in a time of 0.48 s.

  (a) What is the potential difference across the resistor as the loop is collapsed?

  (b) What is the direction of the current in the resistor?



3. Consider the circuit constructed from an ideal battery, and ideal inductor and a resistor as shown. The switch is closed at a time t = 0.

  (a) What is the maximum current drawn from the battery?

  (b) What is the value of the time constant of this circuit?

  (c) At what rate is the current changing when t = one time constant?

  (d) When the current is at its maximum, how much energy is store in the magnetic field of the inductor?



4. Radiation from a point source is found to have an intensity of 855 W/m2 at a receiver located a distance of 5.75 m from the source. The frequency of the signal is measured to be 957 kHz.

  (a) What is the power of the source?

  (b) What is the magnitude of the electric field of the electromagnetic wave at the site of the receiver?

  (c) What is the wavelength of the radiation?



5. Calculate the displacement current in a capacitor consisting of two parallel plates, each of area 0.55 m2, separated by an air gap of 0.83 mm, when the potential between the plates is changing at a rate of 7.5 x 108 V/s.



6. A light ray which has a wavelength in vacuum of 500 nm is incident on the surface of a glass plate and air from inside the glass. The angle of incidence is 34.0o. The index of refraction for this glass is 1.55.

  (a) What is the value of the angle of reflection?

  (b) What is the value of the angle of refraction?

  (c) What is the value of the critical angle for this situation?



7. Two identical tiny conducting balls carry charges of +4.0 x 10-9 C and -3.20 x 10-8 C. They are 3.0 cm apart.

  (a) Compute the force of attraction.

The balls are now touched together and then separated to 3.0 cm again.

  (b) Calculate the magnitude of the force on them now.

  (c) Do the balls now attract or repel?



8. An electric dipole, having a dipole moment of magnitude 1.45 x 10-8 C·m, is in an electric field of strength 750 N/C. The dipole moment vector makes an angle of 35.0o with the direction of the electric field. Calculate

  (a) the magnitude of the torque acting on the dipole and

  (b) the potential energy of the dipole.



9. The figure shows two charges, Q1 and Q2. Assume that Q1 = +1.0 µC, Q2 = -5.0 µC, r1 = 5.0 cm and r2 = 5.0 cm.

  (a) Calculate the electric potential V at the origin of the coordinates. Use the conventional zero.

  (b) Calculate the potential energy of this charge distribution.



10. A long slender wire of uniform cross-section is to be formed from the material in a cube of solid copper 1.85 cm on a side. The resistance of this wire is to be 3.95 ohms. The resistivity of Cu is 1.77 x 10-8 ohm·m.

  (a) Calculate the length of this wire.

Allow a current of 15.0 A to flow through this wire.

  (b) At what rate is heat being produced in this wire?

  (c) How many electrons will flow through a cross-section of this wire in a second?



11. The circuit shown has the following capacitors: C1 = 6.00 µF; C2 = 3.00 µF; C3 = 3.00 µF. The capacitor C1 has a charge of 48.0 µC.

  (a) Find the equivalent capacitance for this circuit.

  (b) What is the battery potential in this circuit?

  (c) Determine the charge that must be on capacitor C3.

  (d) How much energy is stored in capacitor C1?



12. An ideal solenoid is connected to a 12 volt battery and a 6.0 ohm resistor. The solenoid is 0.55 m long and 1.0 cm in diameter with a total of 4500 turns.

  (a) what is the magnitude of the magnetic field at equilibrium inside the solenoid, and

  (b) what is the self inductance of the solenoid?



True-False Questions

On your answer sheet, indicate whether each of the following statements is true (T) or false (F).

13. The electric field of a point charge always points towards the charge.

14. Regions of zero electrical field intensity need not be regions of zero electrical potential.

15. A positively charged, irregularly shaped chunk of copper has a higher electrical potential at its sharpest surface point than at any other location.

16. Lines of B form continuous loops in space.

17. Maxwell’s equations apply only to fields that are constant in time.

18. Electromagnetic waves are transverse.

19. In an electromagnetic wave, the electric and magnetic field vectors E and B are equal in magnitude.

20. In an electromagnetic wave, the electric and magnetic energy densities are equal.

ANSWERS

1.  (a) 0.41 Wb  (b) 0.35 A   (c) 0.19 N

2.  (a) 0.51 V  (b) left

3.  (a) 0.800 A  (b) 0.383 ms   (c) 768 A/s  (d) 1.84 mJ

4.  (a) 355 kW  (b) 803 N/C   (c) 313 m

5.  4.4 A

6.  (a) 34.0o  (b) 60.1o   (c) 40.2o

7.  (a) 1.3 mN  (b) 2.0 mN   (c) REPEL

8.  (a) 6.24 x 10-6 N·m   (b) -8.91 µJ

9.  (a) -720 kV  (b) -0.64 J

10. (a) 37.6 m  (b) 889 W   (c) 9.36 x 1019 /s

11. (a) 3.00 µF  (b) 16.0 V   (c) 2.40 x 10-5 C   (d) 1.92 x 10-4 J

12. (a) 0.021 T  (b) 3.6 mH

13.  F

14.  T

15.  F

16.  T

17.  F

18.  T

19.  F

20.  T