Aneutral spherical conductor of radius a has a concentric cavity of radius b < a, and is centred on the origin. charge q is then transferred to the sphere by contact . a) determine the electric field everywhere (i. e. as a function of radius r).
b) determine the potential everywhere.
c) what is the capacitance of the sphere?
d) how would these answers change if an additional charge was placed at the origin?

Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".