Two identical, small spheres of mass 2.0 g are fastened to the ends of a 0.60m long light, flexible, insulating fishing line. The fishing line is suspended by a hook in the ceiling at its exact centre. The spheres are each given an identical electric charge. They are in static equilibrium, with an angle of 30 between the string halves, as shown. Calculate the magnitude of the charge on each sphere. (Hint: start off by drawing a FULL, DETAILED FBD of one of the charged spheres)
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Thus the magnitude of charge on each sphere is q = 1.2 E - 7 N
Explanation:
Given data:
- Mass of spheres = 2 g = 0.002 Kg
- Length of line = 0.6 m
- Angle "θ" = 30°
Solution:
Ty = mg = 0.002 x 9.8 = 0.0196 N
tan 15° = Tx / Ty =
Tx = Ty tan 15° = 0.0196 tan 15°
Tx = 0.0052518 N
Fe = Tx = 0.0052518 N
Separation distance = 2 x 0.3 x sin (15°)
F = Kq1q2 / d^2 = k.q^2 / d^2
0.00525 N = 8.99 E9 q^2 / (0.15529 m^2)
q = 1.2 E - 7 N
Thus the magnitude of charge on each sphere is q = 1.2 E - 7 N
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