Homework Help: Wire going through a magnetic field

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1. Mar 4, 2015

timnswede

1. The problem statement, all variables and given/known data
A wire carrying 1.5 A passes through a region containing a 2.0 T magnetic field. The wire is perpendicular to the field and makes a quarter-circle turn of radius R= 1/ as it passes through the field region as shown below. Find the magnitude and direction of the magnetic force on this section of wire. Use the coordinate system shown and take the +z-axis out of the page. (Hint: Do Not Integrate)

2. Relevant equations
Fb=ILxB

3. The attempt at a solution
So what I did was I drew a straight line from where the wire enters the field to where it exits. Then I used the Pythagorean theorem to get the length of the wire, which is 1m (assuming meters, could call it units I suppose). Then I used the right hand rule, with ILxB, and got Fb being 90 degrees up and to the right of the wire. So Fb=ILBsin90=3 N.Would this be a correct way of doing it?

2. Mar 4, 2015

rude man

Why did you do that? The length of the wire is obviously not that of your 'straight wire'. And the force on the wire is a vector so you need to express it that way.

Last edited by a moderator: Apr 17, 2017
3. Mar 4, 2015

timnswede

I did it because if I take the integral of a curved wire in a uniform magnetic field it is just the displacement, like in this example http://i.imgur.com/mNSSko3.png. Would that not apply here? I know I can get the length of the wire since it is a quarter circle, but why would the other way not work?

4. Mar 4, 2015

rude man

OK, I see what you did. Interesting apprtoach. But you need to express the force as a vector. You have correctly obtained the magnitude but not the complete vector force.

5. Mar 4, 2015

timnswede

Since Fb is perpendicular to my straight line, it would be 45 degrees above the x-axis right?

6. Mar 5, 2015

rude man

Right.
Would you have gotten the right answer if the B field had pointed in the direction of +z instead of -z? How?

7. Mar 5, 2015

timnswede

Then the Fb is still perpendicular to my straight line, but now it's is below it. So it would be the same magnitude, but 135 degrees below the x axis.

8. Mar 5, 2015

rude man

Right again. I think you have this subject well in hand.