Problem involving charges/coulombs, distance, and force? (and maybe electric field?)?

Question

Points A and B are separated apart by 3 m. Point A has a charge of 2 C, and B has a charge of 3 C. Point C is located somewhere in between points A and B so that the force on C is zero. How far away from point A is point C?

Answer 1

Well, if the net electric force at point C is zero, then the net electric field at point C must also be zero (since electric_force = electric_field*test_charge). (This assumes C can have any charge.)

Recall that electric_field = k * q / r²
Where k is Coulomb's constant, approximately 8.988*10^9 [N*m²/C²], q is the source charge, and r is the distance between the source charge at your point of reference (in this case point C).

Well, since points A and B both have positive charges, then we know equilibrium must be between them (and likewise, if both were negative).

Since electric fields "point toward" negative charges, each respective electric field will point away. So the electric field due to point A must equal the electric field due to point B, since they're "pointing toward" one another.

If you let x be the distance between points A and C, then (3-x) is the distance between points C and B. Plug these distances in for r, and your respective charges in for q, and then solve for x.

Your equation should look something like this:
k*2/x² = k*3/(3-x)²

Then just solve for x.

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For additional practice, you might want to let point A have a negative charge instead. Then, the electric field would equal zero at some point to the left of point A. You could actually solve this problem in exactly the same way, but you will find that x will be a negative value instead (indicating its position relative to A, since we defined the position at A to be zero).

Answer 2

You haven't indicated that there is any charge on point C and, if that's the case, the net force on C is zero no matter *where* it's located.

HTH ☺

Doug

Answer 3

isn't it that factor C might desire to genuinely have a charge? wait... I genuinely have an theory. permit ok = electrostatic consistent and z = charge of C x = distance of C from A [ok(2c)(z)]/(x^2) = [ok(3c)(z)]/((3 - x)^2) fixing... ok. i've got been given something around a million.348 m.