Question

A charge of 23.8 $$\mu C$$ is located at (4.33 m, 5.97 m), and a charge of -12.0 $$\mu C$$ is located at (-4.53 m, 6.77 m). What charge must be located at (2.11 m, -2.92 m) if the electric potential is to be zero at the origin?

Answer 1

For 1st charge, distance to origin = sqrt(4.33^2 + 5.97^2 ) = 7.375m
For 2nd charge, distance to origin = sqrt(4.53^2 + 6.77^2 ) = 8.146m
For 3rd charge, distance to origin = sqrt(2.11^2 + (-2.92)^2) = 3.602m

Potential at origin from 1st charge = kQ/r = k x 23.8x10^-6 / 7.375
Potential at origin from 2nd charge = kQ/r = k x (-12.)x10^-6 / 8.146
Potential at origin from 3rd charge = kQ/r = k x Q x10^-6 /3.602 where Q is in microC

Potential is a scalar, so you can just add the values to get the total; we want total at origin to be zero so:
[k x 23.8x10^-6 / 7.375 ] + [k x (-12.)x10^-6 / 8.146 ] + [ k x Q x10^-6 /3.602] = 0
23.8/7.375 - 12/8.146 + Q/3.602 =
1.754 + Q/3.602 = 0
Q = -1.754x3.602 = - 6.318microC

Answer 2

Answer 3

For 1st charge, distance to origin = sqrt(4.33^2 + 5.97^2 ) = 7.375m
For 2nd charge, distance to origin = sqrt(4.53^2 + 6.77^2 ) = 8.146m
For 3rd charge, distance to origin = sqrt(2.11^2 + (-2.92)^2) = 3.602m

Potential at origin from 1st charge = kQ/r = k x 23.8x10^-6 / 7.375
Potential at origin from 2nd charge = kQ/r = k x (-12.)x10^-6 / 8.146
Potential at origin from 3rd charge = kQ/r = k x Q x10^-6 /3.602 where Q is in microC

Potential is a scalar, so you can just add the values to get the total; we want total at origin to be zero so:
[k x 23.8x10^-6 / 7.375 ] + [k x (-12.)x10^-6 / 8.146 ] + [ k x Q x10^-6 /3.602] = 0
23.8/7.375 - 12/8.146 + Q/3.602 =
1.754 + Q/3.602 = 0
Q = -1.754x3.602 = - 6.318microC