A conducting sphere of radius R carries positive charge q. Calculate the amount of work that would be required to move a small positive test charge q0 slowly from r=4R to r=R/2. Assume that the presence of q0 has no effect on how the charge q is distributed over the sphere. Express your answer in terms of the electric constant ϵ0 and some or all of the variables q, q0, and R.

Suppose a swarm of bees flies through a thunderstorm and they become charged to –10.0 µC each. If there are 5,000 bees in the hive, what is the total electric flux through the walls of the hive? a. b. The Hatfields and McCoys have a historic feud, and now they have physics degrees. Using the figure below, if the bees fly straight up out of the hive and Mr. Hatfield would like to deflect the bees toward Mr. McCoy, in what direction should he apply a magnetic field (into the page or out of the page)? Vbees "leaving x-axis Om 100m 200m Mr. Hatfield hive Mr. McCoy If the bees fly straight up at 0.5 m/s, and a 50 µT magnetic field is applied in the direction you indicated in part (b), what is the magnetic force that the bees experience? (Both strength and direction.) d. When the bees return to the hive they fly straight down into it. If the magnetic field is still applied in the direction of your answer to part (b), in what direction are the bees deflected?

A parallel plate capacitor in air is constructed with two 13 cm x 13 cm square conductors separated by 3 mm. a) Determine the value of the capacitance of this parallel plate capacitor. b) This capacitor is placed across a 12 V battery and allowed to fully charge. What is the value of this charge? To continue, please enter your answer in b) in units of nC.   Round your answer to 1 decimal place.

с A slab of copper of thickness b is thrust into a parallel-plate capacitor of plate area A and plate separation d, as shown in the figure above; the slab is exactly halfway between the plates. NOTE: Express your answers in terms of the given variables using eo and q when necessary. (a) What is the capacitance after the slab is introduced? = W b (b) If a charge q is maintained on the plates, what is the ratio of the stored energy before to that after the slab is inserted? d U₁ Uf (c) How much work is done on the slab as it is inserted? = = (d) Is the slab sucked in or must it be pushed in? [Choose one ▾