Question

A 6.5 C charge is at the origin and a 12.8 C charge is at (9.0 m, 0). Where between these two charges should a third charge be placed so that it experiences zero net force? Does the sign of the charge matter?

*(Answer should be 3.74m)

Answer 1

The two charges are placed along the x axis, one at x = 0 and other at x = 9.0 m, that is, two charges are separated by a distance 9.0 m along the x axis. Let the third charge be q and placed at a distance x from the charge at origin. So, the charge q will be separeted by a distance of (9-x) from the charge 12.8 C. The charge q will experience zero net force if force on q due to 6.5 C and 12.8 C will be equal and opposite, that is, we must have,

k*q*6.5/x² = k*q*12.8/(9-x)²

Or, (9-x)²/x² = 12.8/6.5

Or,   (9-x)/x = 12.8/6.5 = 1.40329

Or, 9-x   = 1.40329x

Or, 1.40329x+x   = 9

Or, 2.40329x   = 9

Or, x   = 9/2.40329 = 3.74

Thus the charge q should be placed at x = 3.74 m in between the given charges.

The sign of the charge q would not matter because whether the charge q is positively charged or negatively charged, the forces on q due to 6.5 C and 12.8 C charges will be oppositely directed.