Question

A charge -Q is between a charge Q and a charge 2Q separated by a distance d. How far from the charge Q is the negative charge if the net force on the negative charge is 0?

Answer 1

As given in question, charge "-Q" is in between charge "+Q" and charge "+2Q".

We assume that charge "-Q" is "x" distance apart from charge "+Q". so, "-Q" will be (d-x) distant from charge "+2Q".

Force on "-Q" by charge "Q" will be ; F₁ = 1/(4π *ε) * (Q*Q)/x²

Force on "-Q" by charge "2Q" will be ; F₂ = 1/(4π *ε) * (2Q*Q)/(d-x)²

As net force is zero, F₁ and F₂ must be equal (We already know that it is in opposite direction)

1/(4π *ε) * (Q*Q)/x²  = 1/(4π *ε) * (2Q*Q)/(d-x)²

1/x² = 2/ (d-x)²

[(d-x)/x]² = 2

(d-x)/x = √2

(d/x) -1 = √2

d/x = √2 + 1

x = d / (√2 +1)