An electron enters a uniform magnetic field, of magnitude 0.23 T, traveling at an angle of 45o with respect to the direction of the magnetic field. Determine the radius and pitch of the helical path if its speed is 3×106 m s-1 Imagine changing this question. What if instead of being given the angle and velocity, you were given the radius and pitch of the helical path. Could you work backwards to calculate the angle and velocity?

21) An electron enters a uniform magnetic field, of magnitude 0.23 T, traveling at an angle of 45o with respect to the direction of the magnetic field. Determine the radius and pitch of the helical path if its speed is 3×106 m s-1
Imagine changing this question. What if instead of being given the angle and velocity, you were given the radius and pitch of the helical path. Could you work backwards to calculate the angle and velocity?
22) Mr Magoo is extremely near sighted and can only see objects 15 cm from his eye. What is the focal length of the glasses he will require?
23) A friend requires reading glasses. You determine that she can see quite clearly objects at a distance of 80 cm from her eyes. If she would like to read a book held 20 cm from her eyes, what focal length glasses would she require?
24) According to a recent Clean Air Task Force’s report, titled “The Toll from Coal, ” pollution from the Bruce Mansfield power plant causes 69 deaths a year. There are 171 673 people residing in Beaver County, where the Bruce Mansfield plant is located.
Is the risk of getting cancer by living near the Fukushima plant worse than the risks from air pollution from living in Pittsburgh?
How much time would you have to spend near the Fukushima plant to have the same excess chance of developing cancer, as the chance of dying from Bruce Mansfield’s pollution?
25) Consider the system shown. A uniformly charged sphere has a spherical cavity removed from it. Find the electric field inside the cavity.
26) A circular loop of wire has a radius of 24 cm and a resistance of 5.2 ohms. It is initially in a 0.6 T magnetic field, with it’s plane perpendicular to the magnetic field, but it is removed from the field in 50.0 ms. Calculate the electric energy dissipated in this process.
27) Superconductivity was discovered on April 8, 1911 by Heike Kamerlingh Onnes, who was studying the resistance of solid mercury at cryogenic temperatures using the recently-produced liquid helium as a refrigerant. In an experiment carried out by S. C. Collins between 1955 and 1958, a current was maintained in a superconducting lead ring for 2.50 yr with no observed loss. If the inductance of the ring was 3.14 10-8 H and the sensitivity of the experiment was 1 part in 109, what was the maximum resistance of the ring?
28) Assuming that the index of refraction of water is 4/3 and that raindrops are spherical, show that the location of a rainbow is approximately 42o above the line from the sun to you.
Hint: Start by ray tracing the light inside the water droplet. Then minimize the deviation angle (the deviation of the outgoing light to the incident light). This is when the light bunches up and causes a bright spot.
29) In the circuit shown, calculate the current through the resistive load (the 100 Ohms resistor).
What is the voltage difference between the two circles, across the 40 Ohm resistor?
30) Graphene consists of a 2D network of carbon atoms just one atom thick. This simple network of atoms results in remarkable physical properties: graphene has higher strength, better thermal conductivity, and greater intrinsic mobility than any other material known. These properties translate into huge technological potential, for example, in transparent electrodes for flatscreen TVs, in fast, energy-efficient transistors, and in ultrastrong composite materials. Hence an enormous global effort is focused on understanding and controlling graphene’s properties with the aim of tailoring them for specific applications.
Imagine the atoms are charged with a charge q, calculate the electric field in the center of a hexagonal unit. Clearly state any assumptions made.
Calculate an expression for the electric potential energy of 6 equally charged particles distributed on the vertices of a hexagon.