# Math Help - Determine the force on a current carrying conductor situated on a magnetic field?

1. ## Determine the force on a current carrying conductor situated on a magnetic field?

calculate the FORCE exerted on a conductor of
Length 20cm which lies at right angles to a pair of magnetic pole pieces having dimensions of 5 cm x 2 cm
Producing a flux of 2 mWb
when the current flowing through the conductor is 4A?

2. Originally Posted by turbod15b
calculate the FORCE exerted on a conductor of
Length 20cm which lies at right angles to a pair of magnetic pole pieces having dimensions of 5 cm x 2 cm
Producing a flux of 2 mWb
when the current flowing through the conductor is 4A?

I'm sorry. I don't quite understand the setup.

The only way I'm making any sense of this is to assume the wire is bent onto a closed rectangle with the magnet in the center. In this case the net force on the closed loop is 0 due to the fact that we can always find a segment of the wire that has an opposing force on it.

But that doesn't make sense to me. Why even mention the current or the flux through the loop?

But if the wire is straight, then the magnetic flux is measured where? In reference to what? The force on different segments of the wire are going to be different. Unless the flux is to be presumed to be constant over all space?

-Dan

3. Calculate the FORCE exerted on a conductor of Length 20 cm, which lies at right angles to a pair of magnetic pole pieces having dimensions of 5cm x 2 cm & producing a flux of 2 mWb, when the current flowing through the conductor is 4A.

length = 20cm
dimensions 5x2=10
3 mWb
current 4A

is it F= B*q*v
Where B= Magnetic induction, q= charge in coulombs, v=velocity of charge perpendicular to field.
which gives F=B*I*L where I=current(A), L=length in metres. (I=ne/t, t=l/v)

4. Originally Posted by turbod15b
Calculate the FORCE exerted on a conductor of Length 20 cm, which lies at right angles to a pair of magnetic pole pieces having dimensions of 5cm x 2 cm & producing a flux of 2 mWb, when the current flowing through the conductor is 4A.

length = 20cm
dimensions 5x2=10
3 mWb
current 4A

is it F= B*q*v
Where B= Magnetic induction, q= charge in coulombs, v=velocity of charge perpendicular to field.
which gives F=B*I*L where I=current(A), L=length in metres. (I=ne/t, t=l/v)

I still don't understand this question. You are given the flux, but not the induction. You are given the dimensions of the magnets and are told they are producing a flux, but not at what point in space. ( $\Phi _M$ is a function of position.) I don't even know what a "pole piece" is supposed to mean.

I can only think of a single situation where the flux might be constant: in the space between two opposing poles of a magnet, where the pole surfaces are very close together. Kind of like a magnetic capacitor. If this is what the problem was intended to be, it was worded very badly.

I will make the assumption that the above is indeed the situation. In this case the flux is constant. To calculate the magnetic induction I will consider the plane surface of one pole of the magnet. This will be perpendicular to the magnetic induction (which also will be constant between the plates) so we have:
$\Phi _M = BA$

$B = \frac{\Phi _M}{A} = \frac{3 \times 10^{-3} \, Wb}{10 \, cm^2} \cdot \frac{100 \, cm^2}{1 \, m^2} = 0.03 \, Wb/m^2$

Now we come to another problem I had thought of: the wire is longer than the region between the magnetic poles. I will assume that the wire is oriented along the 5 cm "axis" of the magnetic plates. In the situation I'm considering, since the magnetic poles are so close together there will be essentially no magnetic induction outside of the plate area. Thus only 5 cm of the wire has a force on it. So:
$F = BIL = (0.03 \, Wb/m^2)(4 \, A)(0.05 \, m) = 0.006 \, N$

Unless I'm missing the obvious (always possible) there are far too many assumptions and there is far too little sense in this problem. I go on record saying that the person who wrote this one should receive 50 lashings with a wet textbook.

-Dan