What charge would have to be fixed at the origin?

[TRVSA]

Homework Statement

A ball of mass m is attached to a rope of length L which has one end at the origin; the ball moves in a horizontal circle at constant speed v0 on a frictionless plane; the velocity is always at 90◦ to the rope. The ball has a charge q, and moves in a constant magnetic field which is directed vertically B⃗ = B0kˆ. At the time illustrated, the ball is at location ⃗r = L cos θˆı + L sin θˆ, with velocity ⃗v = −v0 sin θˆı + v0 cos θˆ.

1. Assume that q = 3.0[C], B0 = 1.0[T], v0 = 5.0[m/s], m = 4.0[kg], and L = 2.0[m], what charge would have to be fixed at the origin in order the tension in the rope became 0?

Homework Equations

T = mv0^2/L + qv0B0

The Attempt at a Solution

I set T to 0, plugged in the values given and tried to solve for q.

 

[PeterDonis]

I set T to 0, plugged in the values given and tried to solve for q.

Please explicitly show what you did and where you got stuck.

 

[TRVSA]

Please explicitly show what you did and where you got stuck.

0 = (4kg)(5m/s)²/2(2.0m) + q(5m/s)(1T)
10 = q

which obviously is not the answer. that was just a shot in the dark. I know q is given as 3.0C.. I just do not know how to solve for the charge at the origin.

 

[PeterDonis]

I know q is given as 3.0C..

That's the charge on the ball. You are not being asked to solve for that. You are being asked to find what charge $Q$ (note the capital letter to show that it's a different charge we're talking about) would have to be placed at the origin for the tension in the rope to be zero. In other words, the charge $Q$, when placed at the origin, should exert the same force on the ball as the tension in the rope does when the charge $Q$ is not there.