Answer to Question #96622 in Electricity and Magnetism for Antonio Rodriguez

Question

Two charges A and B are fixed in place, at different distances from a certain spot. At this spot the potentials due to the two charges are equal. Charge A is 0.19 m from the spot, while charge B is 0.67 m from it. Find the ratio qB/qA of the charges.

Answer 1

Field potential from charge A at a given location

$\text{ } \phi_A=k\cdot\frac{q_a}{r_a}$

Field potential from charge B at a given location

$\text{ } \phi_B=k\cdot\frac{q_b}{r_b}$

by condition of the problem

$\text{ } \phi_A=\phi_B$

or

$k\cdot\frac{q_a}{r_a}=k\cdot\frac{q_b}{r_b}$

$\text{ } \frac{q_a}{r_a}=\frac{q_b}{r_b}$

then

$\frac{q_b}{q_a}=\frac{r_b}{r_a}=\frac{0.67}{0.19}=3.53$

Answer: 3.53