The Force on a Current in a Magnetic Field

[whatadoll]

Homework Statement

The x, y, and z components of a magnetic field are Bx = 0.10 T, By = 0.13 T, and Bz = 0.17 T. A 25 cm wire is oriented along the z axis and carries a current of 4.5 A. What is the magnitude of the magnetic force that acts on this wire?

Homework Equations

F=ILB (sin theta)

The Attempt at a Solution

Well, I have
F= (4.5A)(25e-2 m)(B?) (sin 90)

I don't know which value for B to use or how to incorporate the three values together. I tried using the three B values to find three different force values, but I don't know how to "add" the three together.

This may be totally wrong but when I plugged Bx, By and Bz into the above equation I got
Fx=.01125N
Fy=.01462N and
Fz=.01913N

...but I'm pretty sure this is wrong
Please help

 

[Dick]

The B values are components of a vector. How do you get the length of a vector from its components? The theta in your equation is the angle between the conductor and the magnetic field and is not 90 degrees. How would you compute it?

 

[whatadoll]

Well, if I only had x and y values I would use the pythagoreom theorum(sp) to add the two, but I don't know how to add in the third z component.

As for determining theta I'm thinking that it would be -tan y/x
soo -tan .13/.10 = 52.4 degrees
but what about the z axis?
I'm so confused.

The z axis is what is throwing me totally off. I don't know how what to do with it.

 

[Dick]

There's a pythagorean theorem in three dimensions as well. Take the square root of the sum of all of the components squared. Along the z-axis in three dimensions means it's direction vector can be written as (0,0,1). The easy way to find the angle between two vectors is to use the dot product. cos(theta)=a.b/(|a|*|b|). Does that ring a bell?

 

[nckaytee]

I have the same problem, but with different numbers...

"The x, y, and z components of a magnetic field are Bx = 0.12 T, By = 0.12 T, and Bz = 0.17 T. A 25 cm wire is oriented along the z axis and carries a current of 4.6 A. What is the magnitude of the magnetic force that acts on this wire?"

I can not figure it out with what was discussed in earlier posts

 

[nckaytee]

Someone please help!

So far I have

F=ILBsintheta

F= (4.6)(25)(.24)sintheta

I can not figure out theta :yuck:

 

[Dick]

You have a magnetic field direction of (.12,.12,.17) and the z-axis direction of (0,0,1). Look up the 'dot product'. cos(theta) is related to the dot product of those two vectors and their magnitudes.