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PHYSICS 299
Test 3
Dr. C. L. Davis
Autumn 2003
1)
2)
Two straight conducting rails form a right angle where their ends are joined and lie along the +x,
+y axes. An identical pair of rails moves with speed v0 m/s along a line at  degrees to the +y
axis, as shown, so that a rectangular circuit is formed which increases in size. At t = 0 the area
enclosed by the circuit is zero. A constant magnetic field, B Tesla, is directed into the plane of
the paper.
(a)
Obtain an expression for the area enclosed by the circuit at a time t (t > 0).
(b)
What is the expression for the magnitude of the magnetic flux through the circuit at time t ?
(5)
(c)
Use Faraday’s law of induction to evaluate an expression for the magnitude of the induced emf at
time t.
(5)
(d)
Calculate the magnitude of this emf when t = 10 s, B = 103 T, v0 = 3 cm/s,  = 45o.
[ Remember your trigonometry, 2sin cos = sin2 ]
(e)
Use Lenz’s law to determine the direction of the induced current in the circuit. Indicate the
direction on the above diagram.
(5)
In the LC circuit indicated, the charge on the capacitor at t=0 is q 0.
(5)
(5)
3)
(a)
Write down the expression which describes the charge on the capacitor at time t. (4)
(b)
The circuit oscillates at a frequency of 5 MHz. If the capacitor has a magnitude of 25 µF
calculate the magnitude of the inductance, L.
(6)
[ use 2 = 10 ]
(c)
The energy stored in the capacitor at t=0 is 2 J. What is the magnitude of q 0 ? (5)
(d)
Measured from t=0, how long will it take the energy stored in the inductance to reach 1/4 of its
maximum value ?
(10)
[ sin /3 = 0.86, cos /3 = 1/2, sin /6 = 1/2,
cos /6 = 0.86 ]
The generator in a series LCR circuit provides an emf given by  = msint, where m = 120
V and  = 100 rad/s. The impedance of the circuit is 10  and the current lags the emf by the
angle /3.
4)
(a)
What is the maximum current in the circuit ?
(4)
(b)
Write down an expression for the current as a function of time.
(3)
(c)
Evaluate the average power dissipated in the resistor.
[ sin /3 = 0.86, cos /3 = 1/2, sin /6 = 1/2,
cos /6 = 0.86 ]
(6)
(d)
What is the value of the power factor ?
(4)
(e)
What is the value of R ?
(5)
(f)
Is the circuit predominantly inductive or capacitive ? Explain.
(3)
As a parallel-plate capacitor with circular plates 1 cm in diameter is being charged, the current
density of the displacement current in the region between the plates is uniform and has a
magnitude of 176 A/m2.
[ N.B. Wherever  appears in your answers simply leave it as  ]
(a)
What is the total displacement current between the plates ?
(5)
(b)
Calculate the magnitude, B of the magnetic field at a distance r = 2.5 mm from the axis of
symmetry of this region.
(15)
[ µ0 = 4 x 107 N/A2 ]
(c)
Calculate dE/dt in this region.
[ Use 0 = 8.8 x 10-12 F/m ]
(5)