## HSC Physics DC Motor forces

A forum designed mainly for high school physics students in New South Wales, Australia.
lorrainelewis
Posts: 2
Joined: Thu Dec 04, 2014 10:38 am

### HSC Physics DC Motor forces

Are you able to help me please in deciding which answer is correct for Q12 in 2014 HSC Physics (copy available on BOSTES website).

We have not learnt about this in our HSC Phys course.
but I am assuming they behave the same way??? but I am only guessing.
And do not know why???

What is the answer please and WHY?
a.s.h.
Posts: 110
Joined: Tue Jan 28, 2014 3:50 pm

### Re: HSC Physics DC Motor forces

(The paper is here: http://www.boardofstudies.nsw.edu.au/hs ... hysics.pdf)

Force on the wire has magnitude |F(t)| = BIL.sin θ. B, I and L stay constant over time, and θ also does, being a constant 90° for both cases. The direction of the force changes as the coil becomes vertical due to the split ring commutator (allowing the coil to keep turning). So |F| is constant.

So the force as a function of time for both cases will be a square wave (as the magnitude of the force is constant and direction changes every time coil is vertical), so answer should be C.
lorrainelewis
Posts: 2
Joined: Thu Dec 04, 2014 10:38 am

### Re: HSC Physics DC Motor forces

Why is there no difference between a radial field and a parallel field please????
a.s.h.
Posts: 110
Joined: Tue Jan 28, 2014 3:50 pm

### Re: HSC Physics DC Motor forces

The magnitude of the force of the wire is the same in both cases. The radial field does make a difference though - for torque.

Consider the HSC Physics formula for torque: τ = nBIA cos ϕ, where ϕ is the angle between the plane of the coil and the magnetic field (this formula follows from the definition of torque, τ = r×F). For the parallel field, the angle ϕ changes continuously as the coil turns (at a constant rate if the coil turns at a constant rate), so torque would be a sinusoidal function of time.

In a radial field however, the field is designed so that (theoretically) the field lines are always going to be in the same plane as the coil (ϕ = 0, so cos ϕ = 1 always), so in that case, torque is constant over time, as ϕ is constant.

So the difference that radial field makes is that the angle ϕ between the field and the plane of the coil doesn't change, whereas it does for parallel field.
a.s.h.
Posts: 110
Joined: Tue Jan 28, 2014 3:50 pm

### Re: HSC Physics DC Motor forces

(cont. due to character limit.)

However, the field lines in both cases are perpendicular to side PQ, and it is the angle PQ makes with the field lines (rather than that the plane of the coil makes with the field) that is important for the force on PQ, which is why force is same for both.

The reason why PQ is always perpendicular to the field lines in both cases is that, in both cases, the magnetic field lines lie in the plane of your computer screen (or the page), whereas the edge PQ is perpendicular to the screen/page. (Even in the radial case, regardless of what angle the field lines are making with the horizontal in the plane of the page, they still lie in the plane of the page!)

Since PQ is perpendicular to the screen, and the field lines always lie in the plane of the screen, it follows that PQ is always perpendicular to the field lines.
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: HSC Physics DC Motor forces

Thanks A.S.H. for the explanations.

I think that the problem here is that the sketches don't go with the words. The space between two bar magnets is only a uniform field close to the axis. And for the magnets with the shaped poles shown, the field would only be radial for a relatively small fraction of a cycle.

So, in practice, the shapes of the curves of torque(t) for the two arrangements would be fairly similar. There would be some flattening of the peaks and troughs for the example with curved poles, but it wouldn't look at all like a square wave.

If you disregard the sketches of the magnets, then you can answer this question. But the sketches make it rather difficult: a student is likely to ask 'Why do fairly similar magnet shapes give such very different torque curves?' and that's a very good question.

Joe
Col
Posts: 1
Joined: Sat Feb 21, 2015 4:38 pm

### Re: HSC Physics DC Motor forces

Thanks ASH for pointing out that the diagram is not clear in that the magnetic field is not obviously radial in the left side motor. However I see another problem with the question...
1. I think the motor should rotate the opposite direction to the direction shown in the diagram.
2. The question did not say what the direction of the Force is relative to. What if the force direction is compared to either the wire PQ, or compared to the direction of rotation? I do see that the question does make more sense if the direction is relative to the magnetic field, but it did not say.
3. If you consider points 1 and 2 together, the constant force perhaps should either be shown as a negative force first, then positive, as the force would be in the opposite direction to the rotation shown.

This is shown here: http://www.animations.physics.unsw.edu. ... l#DCmotors.