Three charges +4q, Q and q are placed in a straight line of length l at points at distance 0, l/2 an

Question

Three charges +4q, Q and q are placed in a straight line of length l at points at distance 0, l/2 and l respectively from one end of line. What should be the value of Q in order to make the net force on q to be zero?

Accepted Answer

Charges are placed as shown on time line AC.
For net force on q to be zero, Q must be of -ve sign. If F₁ is force on q due to 4q & F₂ due to Q
Then,    F₁ = F₂         (magnitudewise)
or =
∴    4q = 4Q
or   Q = q        (in magnitude)
∴    Q = −q        (with sign)

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