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Question

A small sphere with mass 1.2 g hangs by a thread between two parallel vertical plates 5 cm apart. The plates are insulating and have uniform surface charge densities +δ and δ . The charge on the sphere is q=9×106C. What potential difference (in V) between the plates will cause the thread to assume an angle of 37 with the vertical as shown in figure?

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Solution

According to the question FBD can be given as


From the FBD we can say that
tan37=FEmg34=qEmgE=3mg4q
To find out potential we multiply both sides with d which is the distance between the plates
E.d=3mgd4q
Putting the values
V=3×1.2×103×10×5×1024×9×106=50 V

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