What Are the Correct Equations for Solving Magnetism Problems?

[shikagami]

I'm confused if I am using the right equations to solve this problem.

P: A singly charged Li^7 ion has a mass of 1.16x10^-26kg. It is accelerated through a potential difference of 500 Volts and then enters a magnetic field of 0.4 Teslas, moving perpendicular to the field. What is the radius of its path in the magnetic field.


I had two different solutions to this problem that has to completely different answers. First, I figured I can use the equation V=(kq)/r. Then I solved for the radius. The second way is by using the volts equation: V=PE/q, which I use to solve for the potential energy. I then used this in the kinetic energy equation KE=1/2mv^2 to solve for the velocity. This velocity I then used in the equation r=(mV)/(Bq). I got 2.88x10^-12 meters for the first solution and 3.44x10^13 meters for the second solution. Which one is right is any?

 

[OlderDan]

What is your understanding of V=(kq)/r? How did you use it?

 

[shikagami]

Well... since I knew how much volts there is, I figured that it is faster to just use that formula where k is the Coulomb constant (8.99x10^9 Nm^2/C^2), then just solve for the radius. Is it possible to use this equation like that?

 

[OlderDan]

Well... since I knew how much volts there is, I figured that it is faster to just use that formula where k is the Coulomb constant (8.99x10^9 Nm^2/C^2), then just solve for the radius. Is it possible to use this equation like that?

No. The r in that equation is distance from a charge q and the V is is the electric potential due to that charge. It has nothing to do with the radius of curvature of a path of a particle, and that V is for a completely dirrerent geometry than what you have.

 

[shikagami]

So is my second solution the right one? or are they both wrong?