Physics 114 Exam I

Answer 3 of the 4 following questions and three of the 4 following probelms. Each question is worth 10 points and each problem is worth 20 points. Clearly mark on the inside cover of your blue book which questions and problems are to be graded.

Questions

1. In the figure below, two uncharged conductors of identical mass and shape are suspended from a ceiling by nonconducting strings. The conductors are given charges q 1 =Q and q 2 =3Q . (a) After charging, which of the angles q1 and q2 that the two strings make with the vertical is larger, or are they equal?

The two conductors are now brought together and made to touch. (b) Which of the two new angles q1' and q2' is the larger, or are they equal? (c) How do the angles q1' and q2' compare with the old angles q1 and q2 ?

2. In the following figure, the dashed line denotes a Gaussian surface enclosing part of a distribution of four positive charges. (a) Which charges contribute to the electric field at P? (b) Is the value of the flux through the surface, calculated using only the electric field due to q 1 and q 2 ,greater than, equal to, or less than that obtained using the field due to all four charges?

3. Rod A is a positively charged insulator. Bob C and a second rod B are in contact with each other and made from conducting material. Rod B is fixed, and C is suspended from a wire and free to swing. Briefly describe what happens when A is brought near B.

4. A hollow insulating cone is placed in a field of field strength E. What is the ratio of the flux through the conical surface A to the flux through the open cross-section B of the cone?

Problems

1. Four point charges are at the corners of a square of side a as shown below. (a) Determine the magnitude and direction of the electric field at the location of the charge q. (b) What is the resultant force on q?

2. An electron travelling with an initial velocity equal to 8.6 x 10⁵ m/s enters a region of a uniform electric field given by 4.1 x 10⁵ N/C. (a) Find the acceleration of the electron. (b) Determine the time it takes for the electron to come to rest after it enters the field. (c) How far does the electron move in the electric field before coming to rest?

3. Consider a long cylindrical charge distribution of radius R with a uniform charge density r. Find the electric field at a distance r from the axis where (a) r>R and (b) r<R.

4. A long, straight wire is surrounded by a hollow metal (i.e. conducting) cylinder whose axis coincides with that of the wire. The wire has a charge per unit length l and the cylinder has net charge per unit length 2l From this information, use Gauss' law to find (a) the charge per unit length on the inner and outer surfaces of the cylinder and (b) the electric field outside the cylinder, a distance r from the cylinder.

Possibly Useful Information

e = 1.6 X 10^-19 C
Dx = x2 - x1, Dt = t2 - t1
	v = dx/dt
	a = dv/dt = d^2x/dt^2
v = vo + at	g = 9.8 m/s^2
x-xo = vot + (½)at^2
v^2 = vo^2 + 2a(x-xo)
x-xo = ½( vo+ v)t
x-xo = vt -1/2at^2	,