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?

Explain vector addition, triangle method and parallelogram method

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

Explain why electric current cannot exist if a current doesn't have a voltage source.