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Q.

Three charges +Q1,+Q2,  and  q are placed on a straight line such that q is somewhere in between +Q1    and    +Q2. If this system of charges is in equilibrium, what should be the magnitude and sign of charge q?

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a

Q1Q2(Q1+Q2)2,  positive

b

Q1+Q22,  positive

c

Q1Q2(Q1+Q2)2, negative

d

Q1+Q22,  negative

answer is C.

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Detailed Solution

Force on Q2 is zero (g should be negative).kQ1Q2R2=kqQ2x2  or  xR=qQ1Force on q is zero:kQ1q(R−x)2=kqQ2x2 or  R−xx=Q1Q2or  Rx=Q1+Q2Q2   or   Q1q=Q1+Q2Q2or  q=Q1Q2(Q1+Q2)2
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Three charges +Q1,+Q2,  and  q are placed on a straight line such that q is somewhere in between +Q1    and    +Q2. If this system of charges is in equilibrium, what should be the magnitude and sign of charge q?