Question

A uniform electric field given by E = (2.60ị – 5.55ņ) x 105 N/C permeates a region of space in which a small negatively charged sphere of mass 1.55 g is suspended by a light cord (see figure below). The sphere is found to be in equilibrium when the string makes an angle 0 = 23.0°. (a) What is the charge on the sphere? (Enter the magnitude.) (b) What is the magnitude of the tension in the cord?

Answer 1

Using equilibrium of the charge under the influence of electric field and gravitational force to form the equation of motion and solve them to find the required charge and magnitude of tension as shown below

Fe = elecoic force charge = q = -191 Noco, 8 = q = -121 [2.6e-5-55ỉ ] *105N/ = 191[-2-ê +5:559] X205 So in horizontal direction, - Fe, sel = Tsino => 191626 X205N/W) = Tsine ---O in vertical direction, Tcose + Feryl = mg Tcose + 19 115.55X105N/C) = (2-55X20-31g 89-8m22) - from © and € 191 = 1.3 x 10-810 b) T = 18.66 X 10-3 n

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