Force on wire due to magnetic field

[nickclarson]

Homework Statement

A straight segment of a current-carrying wire has a current element IL where I = 2.70 A and L = 2.60 cm i + 4.40 cm j. The segment is in a region with a uniform magnetic field given by 1.36 T i. Find the force on the segment of wire. (Give the x, y, and z components.)

Homework Equations

$$\theta = tan^{-1}(y/x)$$

$$F = ILBsin\theta$$

The Attempt at a Solution

Well I am pretty sure there will be no x or y component because the force will be perpendicular in the z direction.

To find the z component I found the angle between the wire and the mag field using:

$$tan^{-1}(4.4/2.6) = 59.421$$

After that I thought you are just supposed to plug everything in:

$$2.7A * .05111m * 1.36 * sin(59.421) = .1615N$$

But it's wrong! I'm not sure what I am doing wrong, the book I am using isn't very good ad explaining. I'm sure it's something simple that I am just overlooking.

Thanks,
Nick

 

[nickclarson]

CANCEL that. I just had the wrong sign. I understand why it should be negative now. This thread can be deleted.

 

[nlightner]

Hello Nick,

Your approach seems correct, but there are a few small errors in your calculations. Firstly, when finding the angle using tan^{-1}, make sure to convert the lengths to meters (2.60 cm = 0.0260 m and 4.40 cm = 0.0440 m). This will give you a slightly different angle, around 59.65 degrees.

Secondly, when calculating the z-component of the force, make sure to use the correct length for L. In this case, L is given as 2.60 cm i + 4.40 cm j, so the z-component will be multiplied by 4.40 cm, not 0.05111 m. This will give you a z-component of 0.281 N.

Overall, your approach was correct, but just make sure to double check your calculations and units. I hope this helps!