Torque on a Current Loop in a B Field

[purduegirl]

Homework Statement

A 119 cm wire carries a current of 1.5 A. The wire is formed into a circular coil and placed in a B-field of intensity 1.9 T.

1) Find the maximum torque that can act on the loop.
2) How many turns must the coil have, so that the torque is maximized?

Homework Equations

1) NIAB(sin theta)

The Attempt at a Solution

For #1, I used the following equation. For area I inputed 2*pi*r*L. I know the length from the information given is 1.19m. However, I don't know how to find the r to solve for the area. Also, I am confused about the turns given. I thought that there would only be one turn because the wire is in a circular coil.

For #2, I would use the answer fron #1 and solve for N.

 

[Gear300]

1) If what you have there is the equation for torque, then N, I, A, and B are apparently constant quantities throughout the process. The maximum torque is when the sine value is 1.

2) For this question, you could use calculus. You have a limit of 119cm of wire, so that limits your area to when the circumference is 119cm. So what they want is a combination of values that will maximize the product N*A.

 

[purduegirl]

1) If what you have there is the equation for torque, then N, I, A, and B are apparently constant quantities throughout the process. The maximum torque is when the sine value is 1.

A is the problem. I can't figure out how to the the area only knowing L and not r.

 

[alphysicist]

Hi purduegirl,

Homework Statement

A 119 cm wire carries a current of 1.5 A. The wire is formed into a circular coil and placed in a B-field of intensity 1.9 T.

1) Find the maximum torque that can act on the loop.
2) How many turns must the coil have, so that the torque is maximized?

Homework Equations

1) NIAB(sin theta)

The Attempt at a Solution

For #1, I used the following equation. For area I inputed 2*pi*r*L.

No, this is not the area they want. This is the surface area of the side of a cylinder, but they don't want the area of the outside of the wire.

Instead, since they are forming the wire into a circle, they need the area of that circle.

So you'll have the formula of the area of a circle, with two unknowns (A and r). Then, what other property of a circle do you know a formula for (that involves the radius)? Since you say you're assuming that there is only one turn, does knowing the total length of the wire help you know the second property?

 

[purduegirl]

I could use the circumference. I know that the circumference is 1.19m. So setting up the equation, C = d*pi, I found that the diamter was 0.3788. I divided that by two and got the radius to be 0.189 m. I tried plugging that radius in into my equation, but I was still wrong. I think there's a problem with my logic about the turn in the circlular loop. They hint given by our homework website was that the number of turns is the variable that we need to take into account.

 

[purduegirl]

Nevermind. I was using the wrong formula for area! THANKS AND HAPPY 4TH OF JULY!