Maximum torque on an electric motor

[Dione]

Homework Statement

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 = ?

Homework Equations

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

µ₀ = 1.257e^-6 N*s²/C²

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.

http://img48.imageshack.us/img48/1562/electricmotor1oc1.th.jpg

Thanks for any and all help,
Dione

 

[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.

 

[baba89]

Hello Dione,

Thank you for your question. To solve this problem, we will first need to understand the concept of torque and how it relates to an electric motor. Torque is a measure of the twisting force that an object experiences when a force is applied to it at a distance from its axis of rotation. In an electric motor, the torque is produced by the interaction between the magnetic field and the current-carrying coil.

To find the maximum torque that the motor can deliver, we will use the equation τ = Fd, where F is the force exerted on the coil and d is the distance from the axis of rotation to the point where the force is applied. In this case, the force is given by F = ILB, where I is the current, L is the length of the coil, and B is the magnetic field strength.

Now, to find the length of the coil, we can use the formula B = µ0(N/L)I/sqrt (1 + (2R/L)2). Rearranging this equation, we get L = (Nµ0I)/Bsqrt(1 + (2R/L)2). Plugging in the given values, we get L = (200*1.257e-6*50e-3)/(0.2*sqrt(1 + (2*2e-2/L)2)). Solving for L, we get L = 0.02 m.

Now, we can plug this value of L into the equation for torque to get τ = (50e-3*0.02*0.2)*(0.02/2) = 0.001 Nm. Therefore, the maximum torque that the motor can deliver is 0.001 Nm.

I hope this explanation helps you understand the concept better. If you have any further questions, please let me know.

Best,