Homework 12

1) In a cathode ray tube, an electron travels in a vacuum and enters a region between two deflection plates where there is an upward electric field of magnitude E = 10⁵N/C.
The deflection plates are 12cm by 3cm and the gap between them is 2.5mm. The plates are charged equally and oppositely and the electron beam is parallel to the long side.
a) Sketch a side view of the plates and draw in the trajectory of the electron.
b) Calculate the acceleration of the electron when it is between the plates.
c) What is the magnitude and sign of the charge on the upper plate and what is the magnitude and sign of the voltage difference?
d) What is the direction and rough magnitude of the E field just ABOVE the centre of the TOP plate.

2) In the figure on the right all the bulbs are identical. Initially the switch is open and all bulbs are equally illuminated. The switch is then closed. a) Describe and explain what happens to the brightness of each bulb. b) Describe and explain what happens to the voltage drop across each bulb. c) Describe and explain what happens to the current in the battery and the total power drawn from the battery.

3) An isolated parallel plate capacitor of area A1 with an air gap of length s1 is charged to a potential V1. A second parallel plate capacitor, initially uncharged, has an area A2 and a gap of length s2 filled with a dielectric of constant ε. you connect a wire from the positive plate of the first capacitor to one of the plates of the second capacitor and a second wire from the negative plate of the first capacitor to the other plate of the second. What is the final potential across capacitor 1?

4) Use Gauss's law to explain why you are fairly safe if you are sitting in a car that is struck by lighting.

5) Consider Oersted's experiment bringing a compass needle close to a wire carrying a current. You lay the compass on the table and lay the wire 5 mm above the needle and align it with the needle as accurately as you can. When you turn on a current in the wire the compass needle deflects 10° to the east. If the horizontal component of the earth's field is 2x10^-5 Tesla what is the current (magnitude and direction) flowing in the wire?

6) A conducting rod of mass m and resistance R rests on two parallel frictionless rails a distance l apart (see figure). There is a uniform magnetic field B perpendicular to rails and rod. At time t=0 the rod is given an initial velocity v0 parallel to the rails. Find the subsequent speed of the rod a) if the rails are insulated from each other and b) if the rails are connected at one end by a wire with no resistance (so that the rod's resistance is the only resistance in the circuit).

Once the rails are connected together, show that the power needed to move the rod along at constant speed is P = Fv = B2l2v2/R and compare this to the power (P = I2R) dissipated in the resistor.