what is the ratio q1/q2

Question

As shown in the figure, three point charges (91, 92. and q3) are fixed on the horizontal x-axis.

The net electric force exerted on që due to the other two charges (q1 and q2) is zero. If d23

= 1.85 012, what is the ratio q1/42?

d12

d23

q1

92

93

C3H7

237

EN

Answer 1

This is an exercise in Coulomb's Law where F = k(q1((q2)/ r^2 with F the force between point charges q is charge and r is separation distance.

So if q3 is situated between q1 and q2, then the net force on q3 is zero, which means the force F23 is equal and opposite to the force F13, the , notation meaning force on 3 due to 1 etc.

Using Coulomb's law we see that F12 = k(q1)(q3) / (r13) ^2 and F23 = k (q3)(q2) / (r23)^2 and here r23 means the distance from q2 to q3 along the axis, etc.

If we set these equal to one another the constant k cancels and so does q3. After rearranging we get the desired ration of q1 /q2 = (d23 / d13) ^2

Note that both charges can be either positive or negative and the net force will still be zero