Ion Thruster Question from Year 12

[physicist101]

Homework Statement

An ion thruster may be used to change the speed of a satellite, through the emmisions of charged particles. Positive xenons ions are accelerated by the potential difference(deltaV) in the region between grid A and grid B as they move towards the right of the diagram.

Xenon ions have a mass of 2.2x10^(-25) kg and a charge of 1.6x10^(-19) C

The potential diffrence in the ion thruster in the region between grid A and grid B increases the speed of an ion by 44 km^(-1)

Calculate the potential difference between Grid A and grid B. (assume that the ions enters the region between the grids with neglible speeds).

Homework Equations

we don't know!

The Attempt at a Solution

sure... with no equations? HELP!

 

[physicist101]

to the eight ppl who looked at it...yes we would like an answer

 

[Astronuc]

How about using conservation of energy. Assume a Xe ion starts at rest, and must be accelerated to a speed of 44 km/s. What is the kinetic energy of the ion at the exit? What is the change in electrical potential energy of the ion?

 

[physicist101]

thanks astronuc, helped a heap.

 

[rwisz]

I understand your frustration with being asked to solve a problem without any given equations. However, in this case, we can use some basic physics principles to determine the potential difference between grid A and grid B.

First, we need to understand the concept of potential difference. It is a measure of the work done per unit charge to move a charge from one point to another in an electric field. In this case, the potential difference is responsible for accelerating the xenon ions.

We also know that the kinetic energy of an object is equal to 1/2 times its mass times its velocity squared (KE = 1/2 mv^2). Since we are given the mass of the xenon ions and the increase in their speed (44 km^(-1)), we can calculate the change in their kinetic energy.

KE = 1/2 * 2.2x10^(-25) kg * (44 km^(-1))^2 = 4.2848x10^(-21) J

We can also use the equation for electric potential energy (PE = q*deltaV) to calculate the potential difference between grid A and grid B.

PE = 1.6x10^(-19) C * deltaV

Setting the two equations equal to each other, we can solve for the potential difference.

1.6x10^(-19) C * deltaV = 4.2848x10^(-21) J

deltaV = 4.2848x10^(-21) J / 1.6x10^(-19) C = 0.0268 volts

Therefore, the potential difference between grid A and grid B is 0.0268 volts. I hope this helps in your understanding of ion thrusters and potential difference.