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How would you measure the electrostatic
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Two very small particles of negligible radii are suspended by strings, each of length 1, from a common point. Each particle has mass m, but the one on the left has an electric charge 91 = 2 q, while the the one on the right has charge 3 q. Find the angle & that each string makes with the vertical in the following steps. (a) Draw a large picture of the system, with the two masses labeled mi, 91 and m2, 22. Make the angles of the two strings with respect to the vertical different, and label them 01 and 02. Both strings have the same length 1. Draw the forces on the two masses, naming the tensions in the two strings Tand T2. Be sure to include the gravitational and electrostatic forces. Showing appropriate com- ponents of forces on each mass (in terms of magnitudes of forces and sines and cosines), write down the net torque of the system about the attachment point of the two strings. In equilibrium, that net torque must be zero. Using this condi- tion, show that i = 02 = 0. (b) Draw a new picture of the system in which the two angles are equal. In addition to this picture, draw two separate free-body diagrams, one for each mass. Include the components of each force along the horizontal and vertical directions, and draw and label the axes (x and y) along those directions. (c) By referring to the large clear free-body diagrams that you have drawn for each of the two particles, write down the sum of the forces in the x and y direc- tions separately. Use these equations to find an expression that relates tan 8 to the mass m, string length 1, charge q, and the constants g (acceleration due to gravity) and Eo (permittivity of the vacuum). 1/3 (d) If 0 is small, show that your result in (a) gives 0 ~ (8.760mg 17)" 3).