Question

Two charges, q1 and q2, are placed a distance D apart (assume they are point charges). A proton is then placed on the line that passes through both charges, and the net force exerted on the proton is zero. How far is the proton from q1?

Answer 1

electric force F = ( K * q1 *q2 ) / r^2 K= 9 * 10^9 N*m^2 / C^2

force on proton due to q1 F1 = ( K *q1*e ) / x^2

force on proton due to q2 F2 = ( K *q2*e ) / ( D - x)^2

net force = 0 F1= F2

so we find q1 / x^2 = q2 / (d-x)^2

( q1-q2) x^2 - 2*D*q1*x + q1* D^2 = 0

we find x = [ D { q1 - ( q1*q2)^(1/2) } ] / (q1 -q2) ..............................Ans

or x = [ D { q1 + ( q1*q2)^(1/2) } ] /(q1 -q2) .............................Ans