# Calculating the work done moving a charge in a magnetic field

## Homework Statement

There are two infinitely long wires A and B, each carries a current of 1 Amp in the same direction. The two wires are 4m apart.
a) Calculate the magnetic field created by the currents in the two wires at points C and D. Point D is 1m away from wire A and point C is 2m away from A.

b) Calculate the work required to move a point charge of +1x10-6 C from point C to point D along the shortest path.

B = µ0I / 2πr
F = qvB
W = qEd
E = F/q

## The Attempt at a Solution

I was able to work out part a) no problem and found the magnetic field at point D is 6.6*10^-8 T and at point C its 2*10^-7 T. My problem is wit part b) :/ How do I find the work done moving a charge from one magnetic field to another? I played around with the formulas a bit and got W = qvBd, but my problem is what do I use for B? Would I be correct in saying that B is the sum of the two magnetic fields? I'm also not given a value for the velocity v so am I going about this the wrong way?

Last edited:

## Answers and Replies

B wouldn't be the sum of the two fields. Think about this problem from the perspective of the charge.

I checked over my figures again and found that there is no magnetic field at point C. The charge is moving 1m towards wire A, from C to D so I know what the magnetic field is. But no matter how many times I go through it I just can't find a value for the work done without a value for the velocity :/