1) A man wants to build a rectangular enclosure for his herd. He only has $900 to spend on the fence and wants the largest size for his money. He plans to build the pen along the river on his property, so he does not have to put a fence on that side. The side of the fence parallel to the fence will cost $5 per foot to build, whereas the sides perpendicular to the river will cost $3 per foot. What dimensions should he choose?

1) A man wants to build a rectangular enclosure for his herd. He only has $900 to spend on the fence and wants the largest size for his money. He plans to build the pen along the river on his property, so he does not have to put a fence on that side. The side of the fence parallel to the fence will cost $5 per foot to build, whereas the sides perpendicular to the river will cost $3 per foot. What dimensions should he choose?
2) Parallel plates are 5 mm apart and 2 m2 in area (you can roll the plates into a cylindrical geometry to make them more compact). A potential difference of 10 kV is applied across the capacitor.
a) Find the capacitance of this parallel-plate capacitor. b) Find the charge stored in this capacitor. c) What is the electric field in the space between the two plates?
3) Copper wire has a diameter of 1.02 mm. It carries a current of 1.67 A to a 200 W bulb. The density of free electrons is 8.5×1028 electrons per cubic meter.
Find a) the current density and b) the drift velocity.
4) A proton moves at a speed of 1000 m/s in a direction perpendicular to a magnetic field with a magnitude of 0.75 T. What is the magnitude of the magnetic force on the proton?
5) Some uranium (atomic number 92) ions (charge +3e) of various isotopes are separated based on their mass. They enter a 0.00002 T uniform magnetic field with a velocity of 105 m/s. What radius of circular motion would uranium-235 have? The isotope mass is approximately 235 u, where u = 1.66 x 10-27 kg.
6) Two protons move past each other. What are the forces on the top proton as they pass? What is the ratio between electric and magnetic forces?
7) The greatest recorded thickness of ice is 4.78 km. It was measured in Antarctica by using the reflectionof radio waves. If the radio waves enters the ice with an angle of incidence of 33 degrees, reflects from the bottom of the ice, and reemerges 4.4 km away, what is the index of refraction for the ice? What would the distance between the entry and exit points be if the radio waves entered the ice from a very thin layer of water that lay over the ice?
8) Imagine a soap film (air-soapy water-air) of 1 m thickness, and refractive index of 1.5 with white light normal to the film. Which wavelengths in the optical range (400 nm to 700 nm) will appear brightest?
9) A thin rod extends along the z-axis from z = −d to z = d. The rod carries a charge Q uniformly distributed along its length 2d with linear charge density λ = Q / 2d. Find the electric potential at a point z > d along the z-axis. Indicate clearly where you have chosen your zero reference point for your potential.
Use the result that E = − V to find the electric field at a point z > d along the z-axis.∇
Can you obtain an expression for the electric potential or electric field when z < d?