Part 1: Do three of four problems, problem 1 - 4.
Problem 1:
A solid sphere of radius R = 40 cm has a total positive charge of 26
mC uniformly distributed throughout its volume.
Calculate the magnitude of the electric field at
(a) 0 cm,
(b) 30 cm, and
(c) 60 cm from the center of the sphere.
Problem 2:
Four long parallel wires carry equal currents of I = 5 A. The figure below is an end view of the conductors.
The current direction is into the page at points A and B and out of the page at points C and D. Calculate the magnitude and direction of the magnetic field at point P, located at the center of the square of edge length 0.2 m.
Problem 3:
Water circulates throughout a house in a hot-water heating system. If the water is flowing at a speed of 0.2 m/s through a 5.0 cm-diameter pipe in the basement under a pressure of 3.0 atm, what will be the flow speed and pressure in a 1 cm-diameter pipe on the second floor 5.0 m above the basement? Assume the pipes do not divide into branches. (1 atm = 101 kPa)
Problem 4:
A capacitor, C = 100 mF, is charged to a potential of 25 kV. The capacitor is then discharged through a 1 kW resistor immersed in and at equilibrium with 500 ml of water. The water is at an initial temperature of 20 oC. Find the final, equilibrium temperature of the water (specific heat 4187 J/kgoC), if the resistor has specific heat of 710 J/kgoC and a mass of 100 g.
Part 2: Do four of five problems, problem 5 - 9.
Problem 5:
You are continually having troubles with the CRT screen of your computer and wonder if it is due to magnetic fields from the power lines running in your building. A blueprint of the building shows that the nearest power line is as shown below. Your CRT screen is located at point P. Calculate the magnetic field at P as a function of the current I and the distances a and b. Segments BC and AD are arcs of concentric circles. Segments AB and DC are straight-line segments.
Problem 6:
Two point charges q and -q are located on the z-axis, at z = +a and z = -a respectively. A grounded conducting sphere of radius b
> a,
centered at the origin, surrounds the point charges.
(a) Find the potential everywhere inside the shell.
(b) Keep qa = p/2 constant and let a go to zero, i.e. produce a dipole
along the z-axis located at the origin. Find the potential
everywhere inside the shell.
Problem 7:
A spherical conductor of radius a is surrounded with a
dielectric shell of outer radius b. The dielectric constant
varies with radius as K = 1 + n(r-a), where n is a constant. A charge
Q is placed on the conductor.
(a) Find the electric displacement and the electric field at all
points in space.
(b) Find the distribution of bound charges in the interior of and
on the surface of the dielectric shell.
(c) Find the total energy stored in the system.
Problem 8:
A proton is accelerated, in vacuum, from rest through a potential U and directed horizontally at a point midway between two horizontal parallel plates which are separated by 0.80 cm and 5 cm long. An electric field is established between the plates by a 10 kV voltage supply and causes downward deflection. Find the minimum accelerating potential U that will avoid the proton striking the lower plate.
Problem 9:
A beam of p+
particles (mp+ = 140 MeV/c2) is
accelerated, so it has momentum pp+ = 2
GeV/c in the laboratory frame. A p+
particle decays into a positive muon (mn+
= 105 MeV/c2) and a muon neutrino (mnm
= 0 MeV/c2) .
(a) What is the energy of the muon in the rest frame of the
p+ particles?
(b) What is the energy of the muon in the laboratory frame if it is found
traveling in the beam direction?
(c) What is the energy of the muon in the laboratory frame if it is found
traveling at 0.25 rad with respect to the beam direction?