Physics 123 Final Exam Fall 2002
Do any Six of the following Seven questions. X-OUT the question you OMIT.

1. A +66.0 mC charge q1 is located 11.0 cm to the right of the origin on the x-axis. A second charge q2 with a magnitude of -21.0 mC is located 83.0 cm to the right of the origin on the x-axis.

(A) What is the magnitude and direction of the electric field at point that is 73.0 cm to the right of the origin on the x-axis?
Ans:{2.04x107 V/m, Right}

(B) If charge q2 is held fixed in place, how much work would it take to move charge q1 to the origin from its initial location?
Ans:{2.30 J}
2. A laser beam of plane-wave electromagnetic waves has a wavelength of 230 nm, a magnetic field amplitude of 18.0 nT, and a cross-sectional area of 5.70 mm 2.
(A) What is magnitude of the amplitude of the electric field and the frequency of the plane-wave beam?
Ans:{1.30x1015 Hz}

(B) How many joules of energy will this laser beam deliver to a 5.70 mm2 target in a time it takes ten wavelengths of the beam to strike the target?
Ans:{1.69x10-21 J}
3. A non-conducting sphere of radius 98.0 cm has a charge of 54.0 mC spread uniformly through out its interior.
(A) What is charge density r(r) at any point inside the sphere?
Ans:{13.7 mC/m3}

(B) Determine the magnitude and direction of the electric field at a point 36.0 cm from the origin?
Ans:{1.86x108 V/m, outward}
4. A 46 volt battery is connected to the circuit shown.
(A) What is the maximum charge on the capacitor after the switch is closed and the current flow reaches its steady state value?
Ans:{4.62 mC}

(B) If the switch is open after the current reaches steady state, what will be the voltage drop across the first resistor R1 exactly 120 ms after the switch is opened?
Ans:{56.6 mV}
5. A complex DC circuit is constructed of two batteries and three resistors as shown.
(A) What is the current flowing through the first resistor R1?
Ans:{89.6 mA}

(B) What is the energy lost to heat by the second resistor R2 in this circuit in 3.80 minutes?
Ans:{227 J}
6. An infinitely long, horizontal, east-west wire carries a sinusoidal current I(t) = Io sin(ω t) with a frequency of 130 Hz and a maximum current of 14.0 A. There is a constant magnetic field of 24.0 mT pointing directly upwards throughout the region of the horizontal plane.

(A) What is the magnitude and direction of the total magnetic field at a point 13.0 cm to the south of the wire when t = 38.0 ms ?
Ans:{31.9 mT, Up}

(B) How much charge flows through the wire to the east in the first half of the current’s cycle, i.e., find the total charge that flows to the east between t = 0 and t = T/2 ?
Ans:{34.3 mC}
7. A 370 Ω resistor and a 108 mH inductor, and a capacitor are connected in series to a current driven sinusoidal oscillator that has a rms voltage of 120 V. The circuit is driven at the resonance frequency of 1700 Hz.
(A) What must be the value of the capacitor in order that the circuit will be in resonance?
Ans:{81.2 nF}

(B) At what moment will the voltage across the inductor be –77.0 V after the system is turned on, i.e. after t = 0?
Ans:{161 ms}

Physics 123 Final Exam Spring 2002
Do any FIVE of the following SIX questions. X-OUT the question you OMIT.

1. A +38.0 mC charge q1 is placed 16.0 cm directly above the origin on the y-axis and a +47.0 mC charge q2 is placed 71.0 cm directly above the origin on the y-axis as shown.

(A) What is the magnitude and direction of the force that charge q1 exerts on q2 ?
Ans:{53.1 N, Upwards}

(B) What is the magnitude and direction of the electric field due to both charges half way between the two charges ?
Ans:{-1.07 MV/m, Down}
2. A 820 pF capacitor is in series with a 120 kΩ resistor and a 3.10 nF capacitor. This combination is connected to a 32.0 DC volt battery.
(A) What is the maximum charge stored capacitor C2 after the switch is closed ?
Ans:{20.8 nC}

(B) How long will it take for the voltage drop across the resistor to equal to 9.50 volts ?
Ans:{94.5 ms}
3. A spherical charge distribution produces a spherical electric potential V(r) = a r2 where a is a constant equal to 160 kV/m2.
(A) What is the magnitude and direction of the electric field at distance 88.0 cm from the origin ?
Ans:{-282 kV/m, towards the origin}

(B) How much work does it take to move a 42.0 mC charge 66.0 cm along a straight line from a point that is originally 88.0 cm from the origin to a point that is 1.90 m from the origin ?
Ans:{19.1 J}
4. An AC circuit consists of an inductor and resistor connected to a 92.0 volt rms source driving the circuit. The impedance of the circuit is 15.0 kΩ and the voltage leads the current by 38.0o.
(A) What is the average power dissipated in this circuit by the resistor ?
Ans:{445 mW}

(B) What is the maximum voltage drop across the inductor ?
Ans:{80.1 V}
5. A beam of plane-wave electromagnetic waves with a wavelength of 590 mm has intensity of 160 mW/m2.
(A) What is the maximum strength of the magnetic field in this beam ?
Ans:{36.6 nT}

(B) How much time does it take between the time when strength of the electric field is at a maximum to the time the strength of the electric field is zero ?
Ans:{0.429 ps}
6. A horizontal, metal loop has a resistance of 28.0 Ω and a radius of 11.0 cm. Through out the interior of the loop, there is a vertical, time-varying magnetic field B = Bo sin(w t) with frequency of 13.0 kHz and an amplitude of Bo = 44.0 mT.
(A) What is the magnitude of the rms current induced in the loop?
Ans:{3.45 A}

(B) What is the magnitude and direction (as viewed from above – either CW or CCW) of the electric field generated in the loop by the changing magnetic field when t = 5.60 µs?
Ans:{177 V/m, CW}