Torque formula for circular coil.

[Jefferson]

Hi Everyone,

For the torque equation

τ = nBIAsin(θ)

The derivation of it comes from a rectangular loop:
https://www.youtube.com/watch?v=xER1_SYql44&start=429
[At the time 7:10]

Why is it then that we can apply this formula to any shape?
e.g. a circular coil instead of a rectangular one.
How does the area 'A' of a circle comes into play for that equation?

Thank you!
-Jeff

[DrDusk]

Hi Everyone,

For the torque equation

τ = nBIAsin(θ)

The derivation of it comes from a rectangular loop:
https://www.youtube.com/watch?v=xER1_SYql44&start=429
[At the time 7:10]

Why is it then that we can apply this formula to any shape?
e.g. a circular coil instead of a rectangular one.
How does the area 'A' of a circle comes into play for that equation?

Thank you!
-Jeff

What do you mean circular loop? I never seen a HSC level question where a circular loop is given.

[Jefferson]

Hi Dr Dusk,

I just meant a coil that has the shape of a circle instead of a rectangle (like the one in the video).

At around 7:10 min, he mentioned that the equation τ = nBIAsin(θ) applies to any area, 'A', (not just rectangular coils), so I was just wondering why that was the case.

Thanks!

[DrDusk]

Hi Dr Dusk,

I just meant a coil that has the shape of a circle instead of a rectangle (like the one in the video).

At around 7:10 min, he mentioned that the equation τ = nBIAsin(θ) applies to any area, 'A', (not just rectangular coils), so I was just wondering why that was the case.

Thanks!

We technically approximate that as a rectangle. The one in the video is considered a 'rectangle' and for all intents and purposes for the HSC it's a rectangle.

Think about it like this. Torque is just multiplying force by distance right. So if you take a rectangle for example you look at the two sides of the rectangle which have torque and multiply their force by the distance from the axis of rotation. Now the force acting on one of the sides is given by





Now if we look at the equation '2d' and 'L' multiplied together actually equals the AREA which gives us the formula in the video. Now if we consider a circle instead of a rectangle, what do we determine as a side? As in what do you define by one 'side' of a circle? It's fully curved everywhere. So we cannot say that the force is given by BILsin(theta) which means the torque on a circular coil is NOT the same as the formula given in the video NBIAsin(theta). So the answer is no we cannot use that formula for a circular coil.

Mod Edit: Merged consecutive posts