Physics 114 1999 Exam 1.

Answer each of the following questions and problems. Each question is worth 10 points each and each problem is worth 15 points. Be sure to show all your work.

Questions

1. Consider the four field patterns shown. Assuming there are no charges in the regions shown, explain why or why not each of the patterns represent(s) a possible electrostatic field.

2. The following figure depicts three charges and a Gaussian surface. (a) Which charges contribute to the net flux through the Gaussian surface? (b) Which of the charges contribute to the field at a given point on the surface? (c) Compare your answers to (a) and (b) and explain why they are the same or different.

Suppose the net charge enclosed by a surface is zero.(d) Does it follow that the field is zero at all points on the surface? (e) Is the reverse true (i.e., if the field is zero at all points on the surface, is the net charge enclosed zero)?

3. A spherical rubber balloon has a charge uniformly distributed over its surface. As the balloon is inflated, how does the electric field E vary (a) outside the balloon, at some point well away from the surface? (b) at the outer surface of the balloon? (c) inside the balloon? Assume the balloon remains spherical during inflation.

4. A charged rod is placed near an uncharged, nonconducting styrofoam sphere suspended from a nonconducting wire, as shown below. Neither the rod nor anything else touches the sphere. (a) Will the rod and sphere exert forces on one another? If so, make a sketch showing the direction of the forces. (b) Would your answer to (a) change if the sphere were made out of conducting material? (c) What is the total charge on the sphere after the rod is placed close to it? (d) Do your answers to (a) and (c) violate Coulomb’s law? Explain.

Problems

1.

q

Four identical point charges (q = + 10.0 mC) are located on the corners of a rectangle. The dimensions of the rectangle are L = 60.0 cm and W = 15.0 cm. Calculate the magnitude and direction of the net electric force exerted on the charge at the lower right corner by the other three charges.

		W
	q

2. An electric field of intensity 3.5 kN/C is applied along the x-axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 7.00 m long if (a) the plane is parallel to the y-z plane; (b) the plane is parallel to the xy plane.; (c) the plane contains the y axis, and its normal makes an angle of 40^o with the x-axis.

3 The following charges are located inside a submarine: 5.00 mC, -9.00 mC, 27.00 mC, and -84.00 mC. (a) Calculate the net electric flux through the submarine. (b) Compare the number of electric field lines leaving the submarine with the number entering it.

4 A 10.0 g piece of styrofoam carries a net charge of -7.00 mC and floats above a very large horizontal sheet of plastic that has a uniform charge density on its surface.[Note - you cannot get a numerical result for parts a and b - just give the expression.] (a) Use Gauss law to calculate the electric field due to the sheet of plastic. Be sure to clearly indicate (on a drawing) the type of gaussian surface you use as well as all the steps in the calculation. (b) Calculate the force on the piece of styrofoam due to the sheet of plastic. (c) What is the charge per unit area on the plastic sheet?

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	,