The distance between two point charges 4q and -q is r. A third charge Q is placed at their midpoint. If the resultant force acting on -q is zero, then Q= .......

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(1) -q. Given: 4q and -q a distance r apart; Q at the midpoint, a distance r/2 from -q. Idea: for zero net force on -q, the force from Q must be equal and opposite to the force from 4q. Force of 4q on -q: an attraction towards 4q, of size (k(4q)(q))/(r²)=(4kq²)/(r²). Q lies on the same side as 4q, so to cancel that pull it must push -q away: Q must repel -q, so Q is negative. Equal sizes: (k|Q|q)/((r/2)²)=(4kq²)/(r²)⇒(4k|Q|q)/(r²)=(4kq²)/(r²)⇒|Q|=q So Q=-q.

The distance between two point charges 4q and -q is r. A third charge Q is placed at their midpoint. If the resultant force acting on -q is zero, then Q= .......

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