A metal sphere hangs from a string and has 4 kg of mass. The sphere has a charge

Question

A metal sphere hangs from a string and has 4 kg of mass. The sphere has a charge of +3.1 µC. A uniform electric field is turned on and directed to the right. A sphere hangs down on a string from a ring attached to the ceiling. Five equidistant parallel arrows travel in straight lines from left to right, and are labelled vector E. (a) Which way does the sphere move? left right (b) What is the electric force on the metal sphere if the magnitude of the electric field is 106 N/C? N (c) When the sphere reaches equilibrium, what is the angle that the string makes with the vertical axis (assuming the same electric field as part (b))? °

Explanation / Answer

a) F = q E

sphere moves right [as q is positive]

b) F = 3.1 * 10-6 * 106

electric force = 3.1 N

c) T cos theta = m g

T sin theta = q E

tan theta = q E / m g

= (3.1 * 10-6 * 106) / (4 * 9.8)

tan theta = 0.079

angle that the string makes with the vertical axis , theta = 4.52 deg

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