Question

Police car is chasing a speed limit violator car with a Doppler radar installed on the roof. Suppose the speed of sound is 300 m/s. When the police car has a velocity v = 10 m/s in the lab frame, it sends a 30 kHz frequency signal.

Suppose we have made a different capacitor, which consists of two oppositely charged small spheres with a radius R separated by a distance D. Assume R << D and the charge is distributed uniformly on the surface of the sphere. Consider an X-axis originating in the center of the first sphere and going through the center of the second sphere. The two centers are at X = 0 and X =D.

3.5 [1pt] Sketch the electric field between X = R and X = D-R.

ANSWER

3.6 [1pt] If once sphere is given a charge Q and the other –Q, calculate the voltage difference between the two spheres.

ANSWER

3.7 [1pt] Calculate the capacitance and express it via R, D, and epsilon_0.

ANSWER

Answer 1

For distance x >R the electric field is same as that from a point source placed at the center of the sphere

k Q/x² . The charges are of opposite sign and the field from both charges will add up it is maximum at the middle of the spheres.

3.6. Potential on the +ve sphere = kQ/R

Potential on the -ve sphere = -kQ/R

voltage difference between the two spheres = 2kQ/R

3.7 Capacitance C = Q/V = Q/(2kQ/R) = R/2k  

= 2R_o