help!

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 0.22 m from the spot, while charge B is 0.54 m from it. Find the ratio qB/qA of the charges.

φ₁=φ₂

k•q1/r1= k•q2/r2
q1/q2= r1/r2

To find the ratio qB/qA of the charges, we can start by using the formula for electric potential due to a point charge:

V = k * q / r

Where V is the electric potential, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge.

Given that the potentials due to charges A and B are equal at a certain spot, we can set up two equations:

V(A) = V(B)

(k * qA) / rA = (k * qB) / rB

We are given the distances: rA = 0.22 m and rB = 0.54 m.

Now, we can rearrange the equation to solve for the ratio qB/qA:

qB/qA = (rB * qA) / (rA * qB)

Plugging in the given values:

qB/qA = (0.54 * qA) / (0.22 * qB)

Now, we can simplify the equation by canceling out qA and qB:

qB/qA = 0.54 / 0.22

Calculating this ratio:

qB/qA = 2.45

Therefore, the ratio qB/qA of the charges is approximately 2.45.