The Net Force on a Test Charge at Equilibrium Due to Two Point Charges

[Larrytsai]

Homework Statement

Two charges, one of 2.50 micro coulomb, and the other of -3.50 micro coulomb, are placed on the x-axis, one at the origin and the other at x=0.600m, as shown in Fig 21.36. Find the position on the x-axis where the net force on a small charge +q would be zero

Homework Equations

F= kq1q1/r^2

The Attempt at a Solution

I tried to equate the force when the distance of the two charges are 0.6m away to the force when the distance is x+0.6

 

[ideasrule]

You can imagine that the charge has to be on the negative x-axis for the force exerted by the positive charge to equal the force exerted by the negative charge. Assume that it's a distance "d" from the origin; then it would be d+0.6 m from the other charge. Proceed from there.

 

[Larrytsai]

yeah i have made that assumption by equating F1=F2, but, i don't understand what's happening after, i cancel my constants, and my charges should cancel so i end up with 1/(0.6)^2 = 1/(x+0.6)^2 , and u end up with 0

 

[ideasrule]

How do the charges cancel? One's 3.5 mC (in magnitude) and the other's 2.5 mC.

 

[Larrytsai]

well i have F1=F2 so its kq1q2/(r)^2 = kq1q2/(r+6)^2

 

[ideasrule]

Don't apply equations without any thought. Think about what the letters in this equation:

kq1q2/(r)^2 = kq1q2/(r+6)^2

stand for. Assuming q1 is the test charge, do the q2's represent the same charge?

 

[Larrytsai]

Don't apply equations without any thought. Think about what the letters in this equation:

kq1q2/(r)^2 = kq1q2/(r+6)^2

stand for. Assuming q1 is the test charge, do the q2's represent the same charge?

im sorry but i do not understand the last part, if we assume q1 is the test charge, so we are able to cancel q1 out?