Question

Three small spheres are placed at fixed points along the x-axis, whose positive direction points towards the right.

Sphere A is at x = 23.0 cm, with a charge of -10.00 microCoulomb
Sphere B is at x = 55.0 cm, with a charge of 2.00 microCoulomb
Sphere C is at x = 57.0 cm, with a charge of -9.00 microCoulomb

(A)If Sphere B is removed. Give the x-coordinate of the point on the x-axis where the field due to spheres A and C is zero? (answer 40.4 cm)

Answer 1

The point where the fields due to A and C cancel has nothing to do with the size of charge B. It also does not depend upon where charge B started out. The point will be between A and C. Let its X-coordinate (in cm) be x. The Coulomb constant k will cancel out, and you can use cm for x and uC for charge. You end up solving this equation:

10/(x-23)^2 = 9/(57-x)^2

(57-x) = sqrt(9/10)*(x-23)
= 0.9487*(x-23)
57 + 21.82 = 1.9487 x
x = ___ cm