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Unformatted text preview: UNEVERSETY OF TORONTO FACULTY OE APPLEED SCEENCE AND ENGINEERING Final Examinations, April 1994 First Year a Program 05 ECE 1508 - Electricity and Magnetism Examiner: S. Dmitrevsky All questions are of equal value and any five constitute a complete paper. Aids: so = 8.85 X 10‘12 Farad/meter, no :2 4 7: X 10-7 Henry/meter. Write in inkl i. A current i(t) plotted in Figure l is driven by a voltage source of negligible internal resistance through a solenoid of negligible resistance, the solenoid parameters being N = 200, A = 2 X 104 m2, l = 0.2 m. Plot the source voltage as a function of times indicating the relationship between the voltage polarity and the direction of current Figure 1. Page 1 of 3 pages Two concentric, connected current carrying quadrants of 0.25 m radius are shown in Figure 2. If the local terrestrial magnetic field is l0'5 Tesla pointing horizontally north, by how much and in what direction will the needle of a compass located at the centre of the quadrants be deflected by a 2 Ampere current circulating in the quadrants as shown in the drawing. Figure 2. A capacitor consists of 0.5 m long, thin coaxial metallic cylindrical shells of 10‘3 m and 3 x 10'3 m radii. The inner of cylinder is coated by a lO’3 m thick layer of dielectric of relative permittivity 2.25. Employing suitable approximation determine: (i) the capacitance of the device, the voltage required to store 10‘6 Joule of energy and, (ii) (iii) the maximum value of the field in the capacitor. A charge Q is uniformely distributed on a straight section of line of length L. Calculate the electric field at a distance h from the line at the middle of the section (i) using the infinite line approximation and, (ii) exactly, using the superposition principle. (iii) Determine at what value of h the error of the approximate result will be 10% of the exact value. du u Aid: ——-——— = ————— j(1+u2)3/2 (1+u2)1/2 Page 2 of 3 pages A 2 x 10‘6 Farad capacitor charged initially to 10 Volt is discharged through a 104 Ohm resistor. Calculate: (i) the time it takes the capacitor voltage to drop to 10% of its original value, (ii) the total energy dissipated in the resistor and the energy extracted from the capacitor in the time interval calculated in (i) above. A 0.15 m x 0.1 m rectangular metallic loop rotates about vertical axis in a horizontal magnetic field of 0.1 Tesla with angular velocity 377 rad/sec. The long sides of rectangle are vertical and at an instant the plane of the rectangle is parallel to the field. Determine: (i) the current flowing in 0.2 Ohm resistor bridging a small gap in the loop and, (ii) the torque exerted on the loop, indicating by means of a suitable diagram the relationship between the direction of the current flow, magnetic field, sense of notation and the torque. Page 3 of 3 pages ...
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