Two identical metallic blocks resting on a frictionless horizontal surface are connected by a light metallic spring having the spring constant 16ON/m and an un- stretched length of 0.32m as shown. A total charge of Q is slowly placed on the system, causing the spring to stretch to an equilibrium length of 0.43m as shown. Determine the value of Q, assuming that all the charge resides on the blocks and modelling the blocks as point charges. State your answer in mC to nearest 0.01 mC. Take electric constant ke to be 8.99x10° Nm?/C2 Hunim (a) (b)

Two point charges of mass m each are suspended in the gravitational field of the Earth by two non-conducting massless strings, each of length 1, attached to the same fixed point. The spheres are given equal charges of the same sign. As a result each string makes angle a to the vertical (see figure below). Write down an expression for the tension of a string Tin terms of Coulomb force Fc between the charges and the angle a. Use the following notation (without the quotes): "/" for division, "*" for multiplication, "+" an "-" as usual. For powers used "^2", while for square root use "sqrt". To indicate that square root applies to the whole expression use brackets - for example, for √AB use sqrt(A*B). For Greek letters such as , a etc. use pi, alpha. For example to get √AB use 1/pi*A^2/B*sqrt(AB). Please use the exact variables given in the conditions of the problem: e.g 1 if L is given, then do not use 1. For subscripts such as Fe simply write "FC" (without the quotes). Please use…

A light, unstressed spring has length d. Two identical particles, each with charge q, are connected to the opposite ends of the spring. The particles are held stationary a distance d apart and then released at the same moment. The system then oscillates on a frictionless, horizontal table. The spring has a bit of internal kinetic friction, so the oscillation is damped. The particles eventually stop vibrating when the distance between them is 3d. Assume the system of the spring and two charged particles is isolated. Find the increase in internal energy that appears in the spring during the oscillations.

A small metal sphere carrying a net charge of Q = -2.00 uC is held stationary by insulating supports. A second small metal sphere with a net charge of Q 2 = +7.80 uC and mass 1.50 g is is held 0.8 m away from the center of the first sphere. Assume the two spheres can be treated as point charges and that you can ignore gravity. If the second sphere is released, how fast will it be traveling when it is 0.6 m away from the center of the first sphere?