A thin washer of outer radius b and inner radius a has a uniform negative surface charge density on the washer (note that > 0 ). a) If we set V (∞) = 0 , what is the electric potential difference between a point at the center of the washer and infinity, V (0) − V (∞) ?

10) A thin washer of outer radius b and inner radius a has a uniform negative surface charge density on the washer (note that > 0 ).
a) If we set V (∞) = 0 , what is the electric potential difference between a point at the center of the washer and infinity, V (0) − V (∞) ?
b) An electron of mass m and charge q = −e is released with an initial speed vo from the center of the hole (at the origin) in the upward direction (along the perpendicular axis to the washer) experiencing no forces except repulsion by the charges on the washer. What speed does it ultimately obtain when it is very far away from the washer (i.e. at infinity)
c) If a positron of charge +e was released a small distance from the center of the hole, along the perpendicular axis to the washer, what might be its fate?
11) An electron is initially accelerated between two plates, with a voltage difference of 300 V between them. It then passes through a hole in a screen into a region where there is a uniform electric field of 900 N/C. If the velocity of the electron is in the same direction as this field, then how far will the electron move before it reverses its direction? What was the maximum speed attained by the electron?
12) Convert a kilowatt hour (kWh) into electron volts (eV).
13) A circular wire loop of 10 turns exists in a plane and has a radius of 1 cm. This wire loop is placed in a solenoid such that the plane of the loop is at 60o to the axis of the solenoid. The solenoid has 100 turns per meter, a radius of 2 cm and a current which varies from 2 A to 1 A in 1 s. Find the emf in the wire loop.
14) A helicopter blade spins at a constant rate of 5.0 revolutions per second about a pivot through one end of the blade. This rotation occurs in a region where the component of the earth’s magnetic field perpendicular to the blade is 30 μT. If the blade is 60 cm in length, what is the magnitude of the potential difference between its ends?
15) A 633 nm laser is shined on a single slit and a screen is placed on the other side of the slit, a distance of 6m from the slit. If the distance between the dark fringes either side of the central bright fringe (between m = 1 and m = -1) is 32 mm, then what is the width of the slit?
16) In a Young’s double slit experiment, you observe a series of bright and dark fringes, the bright fringe to the left of the central bright fringe is 1 cm away from the central bright fringe. The laser used in the experiment is 600 nm. You repeat the experiment with a second laser of wavelength 500 nm, and observe the bright fringe to the left of the central bright fringe to be 0.9 cm away from the central bright fringe.
What is the distance between the two slits in this experiment?
17) Imagine a soap film (n = 1.3) in air ( n = 1) of thickness 1 m. For light incident at 30o to the tangent of the film, which wavelengths will appear most bright (optical range is 400nm to 700nm)? Bumblebees see into the ultraviolet. Which wavelengths of light might appear bright to them which we cannot see?
18) You are spin coating a layer of polymer onto a silicon disk. You want the thickness of the layer to be a micron but have no way of directly measuring it. Looking at the film at an angle of 45 o, what colors might you expect to see the most pronounced and which colors would be absent at the required thickness? The refractive index of the polymer is 1.2 and the silicon wafer is perfectly reflecting.
19) A hollow cylinder of radius R and length l has a total charge Q uniformly distributed over its surface. The axis of the cylinder coincides with the z axis, and the cylinder is centered at the origin.
Obtain an expression for the electric potential as a function of z. Sketch a graph of the electric potential as a function of distance z, for -2l < z < 2l. 20) Dowsing is a form of divination used to locate hidden water wells, buried metals, gemstones, or other objects. A scientific explanation was proposed for this phenomena claiming that moving ones arm in the earths magnetic field could induce an emf along the arm of the dowser and cause muscles to twitch and the dowsing rod to move. The earths magnetic field could be slightly higher over water or other conducting materials, causing muscles to twitch over these objects (almost like a human metal detector). Use your knowledge of electricity and magnetism to theoretically investigate this phenomena. Useful information for this question will include the action potential (voltage) required for muscle contraction which is 10 mV and the earths magnetic field (in Pittsburgh) is 55 T. Are you able to generate this potential in your arms by moving them in the earth's magnetic field?