=========================preview======================
(PHYS013)[2008](s)final~1910^_10534.pdf
Back to PHYS013 Login to download
======================================================
Problem No.1
(1) Two infinite straight wires are charged uniformly with negative charge density . They are positioned along the two edges of a cubic as shown by the two grey lines in the left figure. (a) Write a vector expression of the electric field at points A, B, C and D, respectively. The coordinates of the four points are A(a/2,0,0), B(0,a,0), C(a,0,a), D(a,0,-a). (b)Draw the field vectors in the figure.
(2) Constant current of I pass through the two wires, as shown in the right figure. (a) Write a vector expression of the magnetic field at points A, B, C and D, respectively. The coordinates of the four points are A(a/2,0,0), B(0,a,0), C(a,0,a), D(a,0,-a). (b)Draw the field vectors in the figure.
Problem No.3
A parallel-plate capacitor consists of two discs of radius S separated by a distance d0. Assume S>>d0, so the electric field is uniform inside the two plates and reduced to zero outside the plates. Vertically 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.
(1) The switch is closed at t=0, write an expression of magnetic field at A and B in terms of .V, R, S, rA (rB), d0 and t, respectively.
(2) Following (1), keep the switch closed and move the two plates away from each other at a speed of v. (S>>d remains) Write an expression of magnetic field at A and B in terms of .V, R, S, rA (rB), d0, v and t, respectively.
(3) Following (1), open the switch and move the two plates away from each other at a speed of v. (S>>d remains) Write an expression of magnetic field at A and B in terms of .V, R, S, rA (rB), d0, v and t, respectively.
Problem No.4
A long solenoid creates a magnetic field inside of it. Consider a solenoid with 100 turns of wire per cm (n=100 cm-1 ).
(1) If a current of 2A runs through it, what is the field inside?
(2) Let the radius of the solenoid be R1=2 cm, the radius of a small loop inside it be R2=1.5 cm and the radius of a big loop outside it be R3=5cm. Find the magnetic flux through the two loops.
(3) Now suppose that the current is decreases at a constant rate from 2A to zero over a time of 0.2 seconds. What is the EMF induced in each of the two loops?
(4) At the same condition of (3), what is the EMF induced in each of the two loops if (a) the loop diameter is doubled (b) the loop is tilted 30 from their initial orientation ?
Problem No.5
The following experiments played crucial roles in unraveling the atom structure.
(1) In J.J. Thomsons experiment, electrons, accelerated by a potential difference .V, pass through two parallel plates that are 5.0 mm apart and 3.0 cm long. A 3.0 cm wide, 1.0 mT magnetic field overlaps the parallel plates, and is perpendicular to the electric field. When the potential difference between the two plates is zero, the electron is deflected by 2.0 mm from the center as it