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 0.24 m from the spot, while charge B is 0.37 m from it. Find the ratio qB/qA of the charges.
To find the ratio qB/qA of the charges, we can use the concept of potential due to point charges. The potential (V) at a certain spot due to a point charge is given by the equation:
V = k * q / r
Where:
- V is the potential at the spot
- k is the electrostatic constant (k ≈ 9.0 × 10^9 Nm^2/C^2)
- q is the charge of the point charge
- r is the distance from the point charge to the spot
Given that the potentials due to both charges A and B are equal at the spot, we can set up the following equation:
V(A) = V(B)
k * qA / rA = k * qB / rB
Since the electrostatic constant (k) is the same on both sides of the equation, we can cancel it out:
qA / rA = qB / rB
Now, let's substitute the given distances:
rA = 0.24 m and rB = 0.37 m
So, the equation becomes:
qA / 0.24 = qB / 0.37
To find the ratio qB/qA, we can solve this equation for qB/qA:
qB/qA = (0.37 / 0.24) = 1.54
Therefore, the ratio qB/qA of the charges is approximately 1.54.