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A positive charge +q is located at the point x = 0, y = -a, and a negative charge -q is located at the point x = 0, y = +a.

(a) Show the positions of the charges in a diagram.

(b) Derive an expression for the potential V at points on the x-axis as a function of the coordinate x. Take V to be zero at an infinite distance from the charges.

(c) Graph V at points on the x-axis as a function of x over the range from x = -40 to x = +40.

(d) What is the answer to part (b) if the two charges are interchanged so that +q is at y = +a and -q is at y = -a?

A round cone with half-angle ? = 30° and the radius of the base R = 5.0 cm rolls uniformly and without slipping over a horizontal plane as shown in Fig. 1.8. The cone apex is hinged at the point O which is on the same level with the point C, the cone base centre. The velocity of point C is v = 10.0 cm/s. Find the moduli of

(a) The vector of the angular velocity of the cone and the angle it forms with the vertical;

(b) The vector of the angular acceleration of the cone.