Force of a magnetic field on a current

[rudders93]

Homework Statement

Hi, I'm confused about the formula to find the magnetic force exerted on a current by a magnet, given by the formula F = number of wires (n) * current in each wire (I) * length of wire (l) * strength of magnetic field (B) so: F = nIlB

It also says that only the component of the magnetic field that is perpendicular to the current causes the force.

So I was wondering, the book says the l value changes depending on the location of a magnet, so if the wire is 8cm long and the field is perpendicular (and I assume 8cm long?) the l value is 8*10^-2m. However if the wire is parrellel to the field then the l value is 0. So I'm abit confused as to what the l means. So how does l change if the field is at an angle to the wire, can it be? Like if it's at an angle of 30 degrees to the wire does that mean I have to multiply the value of l by sin30 to get the verticle component? Or is the books definition of l abit loose and does it refer to like the length of the wire in the field? But how does this relate if the field is at an angle?

Sorry if my questions are confused, I'm very confused myself :( Thanks!

 

[Gear.0]

It's because the base equation that they derive the one they gave you from has a cross product. It is:
$$\vec{F} = q\vec{v} \times \vec{B}$$
Which is the same as:
$$F = (qv)(B) sin(\theta)$$

Then it can be shown that the qv is equivalent in your case to (nIL)
So you should use this instead:
F = nILB*sin(theta)
where theta is the angle between the wire bundle and the direction of the magnetic field.
L is just the length of the wire. It doesn't actually change, but it looks smaller to the magnetic field if it is not perpendicular.
So instead of doing it the way they told you where L changes, just use L as a constant and use the equation I wrote with the sin(theta). That will take care of it for you.

I believe they tried to explain this to you, if the wires are perpendicular to the magnetic field then theta=0 and sin(0) = 0 so F=0 Because you have no current traveling perpendicular to the magnetic field. But the more you turn the wire the larger the force will become until it is perfectly perpendicular then it will be a maximum.

and if you look again at the second equation I wrote, it should all make sense. Because that shows that the force is only caused by charged particles moving in a direction perpendicular to the magnetic field, and if they are moving parallel then there is no force. This is just a property of magnetic fields.
So it should be easy to see that this would require a current carrying wire to be perpendicular too because the wire is basically just small moving charged particles.

 

[rudders93]

Ah I see. Thanks!