Finding the change in velocity through a potential difference

[Patches1532]

Homework Statement

Question states: A singly charged ion of unknown mass moves in a circle of radius 12.5 cm in a magnetic field of 1.2 T. The ion was accelerated through a potential difference of 7 kV before it entered the magnetic field. What is the mass of the ion?

Relevant Equations

qB=mv/r

We're given the equation qB=mv/r which is simple enough. I just don't know how to find the velocity given the acceleration through a potential difference. I tried using the radial acceleration equation given to me but I end up with the square root of a negative...and that breaks math... I assume you're first supposed to convert to volts 7kV=7000V, but what equation do I use after that? Any help would be appreciated. Thanks.

 

[kuruman]

Use energy conservation assuming that the particle stated from rest. You may have to review the equation for a charged particle's potential energy in an electrostatic field. It's the equivalent of the gravitational $mgh.$

 

[Patches1532]

I ended up putting a negative in the radial acceleration equation in my notes...I missed these classes and copied notes from a friend. In our book it has it as a=v^2/r which will allow me to solve for V. Thank you for the help.

 

[kuruman]

I ended up putting a negative in the radial acceleration equation in my notes...I missed these classes and copied notes from a friend. In our book it has it as a=v^2/r which will allow me to solve for V. Thank you for the help.

I thought you had difficulty finding the velocity of the particle when it enters the magnetic field. That is calculated using the 7000 V potential difference and is not related to $v^2/r.$

 

[Patches1532]

Then maybe I'm misunderstanding the notes. So in the question, we're given B, r, and p.d. and we are asked to solve for mass (m). In our notes, the only equations it gives us are for radial acceleration, F of the magnetic field=qvBCos(theta), F=ma, and qB=mv/r. We're not told how to plug in p.d. into any equation.

 

[kuruman]

Are you always given all the equations you need to solve a problem? In most curricula electrostatics comes before magnetism and students are expected to have learned the earlier lessons. Here is something to refresh your memory. Concentrate on the section "Conservation of energy".
https://courses.lumenlearning.com/p...ectric-potential-energy-potential-difference/

 

[Patches1532]

Yes that rings a bell. I'll look at the link and try to figure it out. Thank you for your time.