Wire going through a magnetic field

[timnswede]

Homework Statement

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)

Homework Equations

Fb=ILxB

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?

 

[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.

 

[timnswede]

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.

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?

 

[rude man]

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?

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.

 

[timnswede]

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.

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

 

[rude man]

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

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

 

[timnswede]

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

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.

 

[rude man]

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.

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