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 T in 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 7, 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 if L is given, then do not use 1. For subscripts such as Fc simply write "FC" (without the quotes). Please use "Display response" button to check the you entered correct expression, before submitting your answer. 3 d A

Two small identical conducting spheres are placed with their centers 0.64 m apart. One is given a charge of 12 ✕ 10−9 C, the other a charge of −19 ✕ 10−9 C. (a) Find the electrostatic force exerted on one sphere by the other. magnitude  N direction  ---Select--- attractive repulsive (b) The spheres are connected by a conducting wire. Find the electrostatic force between the two after equilibrium is reached, where both spheres have the same charge. magnitude  N direction  ---Select--- attractive repulsive

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 Q 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 T in 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 л, α etc. use pi, alpha. For example to get 14√AB use 1/pi*A^2/B*sqrt(AB). Please use the exact variables given in the conditions of the problem: e.g if L is given, then do not use 1. For subscripts such as Fc simply write "FC" (without the quotes). Please use…

Two hard rubber spheres, each of mass m = 16.3 g, are rubbed with fur on a dry day and are then suspended with two insulating strings of length L = 5.50 cm whose support points are a distance d = 3.21 cm from each other as shown in the figure below. During the rubbing process, one sphere receives exactly twice the charge of the other. They are observed to hang at equilibrium, each at an angle of ? = 10.9° with the vertical. Find the amount of charge on each sphere. (Assume the two spheres have charges q1 and q2 = 2q1)