A. consider a charge q fixed in place at the origin that creates an electric field in the surrounding region. we call a charge which gives rise to the electric field the source charge. you bring a small charge q from infinite distance to a distance r from the source charge adiabatically, that is, infinitely slowly such that the electric field due to the source charge is not disturbed. this small charge q is called a test charge. now answer the following questions. all of your answers will be in terms of q, q, r and the dielectric constant εo, as appropriate and be careful about your signs. 1. what is the electric potential energy of the charge q as a function of the distance r away from

F500 j of energy were added to 1 kg of each of these samples, which would experience the least temperature increase?

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 ⇒

Aclarinetist, setting out for a performance, grabs his 3.350 kg clarinet case (including the clarinet) from the top of the piano and carries it through the air with an upward force of 24.65 n. find the case's vertical acceleration. indicate an upward acceleration as positive and a downward one as negative.