=========================preview======================
(PHYS013)[2009](s)final~1910^_10537.pdf
Back to PHYS013 Login to download
======================================================
Final examination PHYS013 (100 points = 100, Full grade)
Attentions:
(1) Detail steps should be given in your solutions! Grades are given according to calculation steps.

(2) Make clear drawings.

(3) Hand writing should be clear and recognizable (Do not use pencil for writing)



Problem No.1 (10 points)


(1) Draw a circuit diagram using the standard signs for the above circuit in which a and b are two identical light bulbs. (4 points)

(2) Describe the changes of the brightness of the two light bulbs when the switch is closed. (3 points)

(3) Following (2), describe the changes of the brightness of the two light bulbs when the switch is opened. (3 points)



Problem No.2 (15 points)


An infinite long solenoid of radius R1=2 cm with 100 turns of wire per cm. A current I varying as a zigzag function as shown in the right figure runs through it ( Imax=2A, T=0.2 s). The current shown in the left figure is at t=T.
(1) Plot the magnetic fields inside and outside the solenoid as a function of time, defining positive field directing from the left to the right. (3 points)
(2) The radius of a small loop inside the solenoid is R2=1.5 cm and the radius of a big loop outside is R3=5cm. Plot the EMF induced in each of the two loops as a function of time, defining clockwise as positive while viewed from the left to the right. (6 points)
(3) Calculate the EMF induced in each of the two loops if (a) the loop diameter is doubled (b) the loop is tilted 30 from its initial orientation. (6 points)
Problem No. 3 (10 points)


An infinite long conductor wire is in plane and parallel with a rectangular conductor loop of sides a and b. The distance between the wire and the loop center is r.
(1) Calculate the mutual inductance of this system. Plot the mutual inductance as a function of r (r: from Ca to +a ) (4 points)

(2) When the loop is rotated along the vertical axis passing through its center by an angle , plot the mutual inductance as a function of (0<<2) (only consider the situation of r>a/2). (3 points)

(3) When the loop is rotated along the horizontal axis passing through its center by an angle , plot the mutual inductance as a function of (0<<2) (only consider the situation of r>a/2). (3 points)



Problem No.4 (20 points)


A parallel-plate capacitor consists of two discs of radius S separated by a distance d0 (S>>d0). Two points A and B are located between the two plates. A is inside the plates with a distance rA from the center. B is outside the plates with a distance rB from the center. Initially the capacitor is charged by Qmax at the upper plate and CQmax at the bottom plate.
(1) The switch is closed at t=0, write an expression of magnetic field at A and B in terms of L, Qmax, S, rA (rB), d0 and t. (Neglecting energy loss due to radiation) (10 points)
(2) Consider the inductor L is a solenoid containing 500-turn, 25.0 cm long and 1.00 cm radius co