Three point charges, -6.35 10-9 C, -8.20 10-9 C, and +7.75 10-9 C, are fixed at different positions on a circle. The total electric potential at the center of the circle is -2210 V. What is the radius of the circle?
To find the radius of the circle, we need to use the formula for electric potential due to point charges. The electric potential at the center of the circle is the sum of the electric potentials due to each point charge.
The formula for electric potential due to a point charge is:
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 to the center of the circle.
We have three point charges, so the total electric potential at the center of the circle is:
V_total = V1 + V2 + V3
Substituting the values given:
V_total = (k * q1 / r1) + (k * q2 / r2) + (k * q3 / r3)
Where q1 = -6.35 x 10^-9 C, q2 = -8.20 x 10^-9 C, q3 = +7.75 x 10^-9 C
We know that V_total = -2210 V.
So the equation becomes:
-2210 = (k * (-6.35 x 10^-9) / r1) + (k * (-8.20 x 10^-9) / r2) + (k * (7.75 x 10^-9) / r3)
Now, we just need to solve this equation to find the values of r1, r2, and r3, and then find the average of the three radii to get the radius of the circle.