# Maximum torque on an electric motor

1. Oct 6, 2008

### Dione

1. The problem statement, all variables and given/known data
In an electric motor, a coil with 200 turns of radius 2 cm can rotate between the poles of a magnet. The magnetic field strength is 0.2 T. When the current through the coil is 50 mA, what is the magnitude of the maximum torque that the motor can deliver?

Variables
N = 200 turns
R = 2e-2 m
B = 0.2 T
I = 50e-3 A

τ = ?

2. Relevant equations

F = ILB
B = µ0(N/L)I/sqrt (1 + (2R/L)2)

µ0 = 1.257e-6 N*s2/C2

3. The attempt at a solution

I first wanted to find what the L was so I could solve for the force. So I tried that. That didn't work out too well. I then tried anything. I'm still not sure I entirely understand the concept. I cannot receive credit for the problem even if I get it right anymore, but I'd like to know how to handle this if it pops up on the exam.

Thanks for any and all help,
Dione

2. Oct 6, 2008

### marcusl

The torque arises ultimately from the Lorentz forces on the charges moving at velocity v within the wires
$$\vec{F}=q\vec{v}\times\vec{B}$$.

Look in your text, or in a book like Reitz and Milford, Foundations of Electromagnetic Theory. You'll see that, for a loop or coil, the torque T becomes proportional to coil current I and area A
$$\vec{T}=I\vec{A}\times\vec{B}$$.
$$I \vec{A}$$ is defined to be the magnetic moment.

Last edited: Oct 6, 2008
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