Voltage required to produce ions

[ted182]

Voltage required to produce ions...

Homework Statement

Ions with a charge of +2e travel at a speed v=6.4x10^6 m/s perpendicular to a magnetic field with a strength of 5.4T.

What is the voltage required to produce ions with that speed?

Homework Equations

1eV=1.6x10^-19 Joules

The Attempt at a Solution

This is not all of the question -- the lesson deals mainly with direction changes and forces in magnetic fields. I answered everything related to the magnetic fields with relative ease, but this voltage problem is a curve ball. I was supplied with no prior info. on accelerating protons, but found the above relation between joules and electronVolts. I know the speed and the charge of the particles (3.2x10^-19), but I don't know how to calculate the Joules required to accelerate the protons.

 

[AvroArrow]

Can someone provide guidance? The voltage required to produce ions with that speed is the energy required to accelerate the ions divided by the charge of the ions. Since v=6.4x10^6 m/s, the energy required to accelerate the ions is given by E=1/2mv^2, where m is the mass of the ion. The mass of an ion is equal to the charge of the ion (in this case, +2e), multiplied by the mass of an electron. Thus, the energy required to accelerate the ions is E = 1/2*(2e)*(6.4x10^6)^2, or E = 3.072x10^-14 J. This energy can be converted to voltage by dividing by the charge of the ion (2e): V = E/2e = 1.536x10^-14 V.

 

[nlightner]

To calculate the voltage required to produce ions with a speed of 6.4x10^6 m/s, we can use the equation for kinetic energy (KE) which is KE= 1/2mv^2. In this case, the mass (m) would be the mass of the ions, which is not given in the question. However, we can use the charge (q) and the speed (v) to calculate the mass using the equation qvB=mv^2/r, where B is the magnetic field strength and r is the radius of the circular motion of the ions. Since the ions are traveling perpendicular to the magnetic field, r would be the radius of the circular motion.

Once we have the mass, we can plug it into the equation for kinetic energy and solve for the voltage required. Keep in mind that the voltage required would be equal to the kinetic energy of the ions, since the ions are gaining this energy from the electric field.

So, the final equation would be:

V= KE/q= (1/2mv^2)/q

I hope this helps! Let me know if you have any other questions.