Three charges q , Q and +4q are placed in a straight line of length d at points at distance 0 , d 3 , 2d 3 respectively. In order to make the net force on q be zero, the value of Q should be

Step-by-step solution

The charges q , Q , and +4q are placed along a straight line of length d . To satisfy the total length d and the given intervals, their positions are x = 0 , x = d 3 , and x = d respectively. The distance between q and Q is d 3 , and the distance between q and +4q is d . The net force on the charge q at x = 0 is the sum of the electrostatic forces exerted by Q and +4q . The force on q due to Q is: F₁ = 1 4 ₀ qQ ( d 3 )^2 = 9qQ 4 ₀ d^2 The force on q due to +4q is: F₂ = 1 4 ₀ q(4q) d^2 = 4q^2 4 ₀ d^2 For the net for