Two equal point charge Q=?2 microcoulomb are placed at each of the two corners of a square and equal point charges 'q' at each of the other corners.What must be the value of 'q' so that the resultant force on Q is 0.

Asked by anshuman dutta | 24th Apr, 2014, 09:29: AM

Expert Answer:

 
Each side of square is of length b.
Hence, distance of charge Q from opposite charge Q is PR = square root of straight b squared plus straight b squared end root equals square root of 2 straight b
We can see that if the resultant force on charge Q placed at point R is zero, then charges at Q and S have to be negative.
 
Forces FP, FQ and FS act on the charge Q at point R. Force FP will have vertical and horizontal components.
 
Hence, we have
 
straight F subscript straight S equals straight F subscript straight P cos 45 degree straight F subscript straight Q equals straight F subscript straight P sin 45 degree
 
Thus, we have
 
fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator minus qQ over denominator QR squared end fraction equals fraction numerator 1 over denominator 4 πε subscript 0 end fraction QQ over PR squared cos 45 fraction numerator minus straight q over denominator straight b squared end fraction equals straight Q over open parentheses square root of 2 straight b close parentheses squared fraction numerator 1 over denominator square root of 2 end fraction equals fraction numerator straight Q over denominator 2 square root of 2 straight b squared end fraction therefore straight q equals fraction numerator minus straight Q over denominator 2 square root of 2 end fraction

Answered by Romal Bhansali | 7th May, 2014, 12:34: PM

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