Magnetism Questions

[kenhung123]

I don't exactly understand what is theta in the F=ILB formula. Apparently if the angle of a wire changes the current is still considered perpendicular to the earth's magnetic field?

[appianway]

Not really. F= IL x B, which can be written as IL sin (theta) B, where theta is the angle between the magnetic field and the wire. So if they're parallel, sin(theta) = 0, and hence the wire experiences no force.

[kenhung123]

Seemed a bit strange to me also. Question 3 multi choice tripped me up. I thought it was less?

[kenhung123]

Yea so...does chaning the angle of current change the force?

[Whatlol]

Yes the changing angle can change the force but if you look at the question im fairly sure the current is flowing from east to west, but the magnetic field of earth is south to north so the angle between the magnetic field and current isn't changing. (to be honest im not actually 100% sure but i think that may be correct)

[kenhung123]

Does it mean:

[kenhung123]

Anyone pleas help?

Also would like to ask is there a particular reason the magnetic field runs from south to north in solenoid?

[mark_alec]

Also would like to ask is there a particular reason the magnetic field runs from south to north in solenoid?

There is no particular reason it should run any way. That will depend upon the direction of the twists, the direction of the current and the charge of the current.

[kenhung123]

In the case below, can we assume direction of magnetic field is same as current while from south to north?

[QuantumJG]

The magnetic force is defined as the cross product of the charge's velocity (v) with the magnetic field (B) and multiplied by it's amount of charge (q).

I.e.

F = q (v x B)  

Now a cross product is a vector constructed that is perpendicular to both other vectors (why specialist maths teaches dot products and not cross products is beyond me).

Now for theta. Let's say the particle's velocity is at an angle θ away from the field lines. If θ = 0 there is no force on the particle, but if θ= the force is at maximum. So we need to do a vector projection where the component parallel to the field is vcos(θ) (I.e. This component has no force acting on it) and the component perpendicular to the field is vsin(θ) (I.e. The component that feels the force).

So:

|F| = q|v||B|sin(θ)

Now to get the formula you have let's say we have a wire of length L and defined v as:

|v| =

And there is a current i flowing through the wire defined as:

i =

So now we can say

iL = q|v| (I'll leave it to you to do the manipulations to show yourself this is true).    

So the formula:

|F| = iL|B|sin(θ)

Should come out easily and make sense.

Anyway I hope this helps.

[kenhung123]

Thank you. Nice comprehensive explanation