Magnetic Field - Torque on a Current Loop

[calvert11]

Homework Statement

A circular coil of 720 turns and area 0.6 m^2 is in a uniform magnetic field of 0.63 T. The maximum torque exerted on the coil by the field is 0.0026 N · m.

a) Calculate the current in the coil.

b) Assume the 720 turns of wire are used to form a single-turn coil with the same shape but much larger area. What is the current if the maximum torque exerted on the coil by the field is 0.0026 N · m?

NOTE: Sigfigs do not matter

Homework Equations

T = IABn

The Attempt at a Solution

Part A:
I solved by substitution using the equation T = IABn, getting T = 9.5532e-6 N · m (answer is correct)

Part B:
This is the part I'm having trouble with. I thought I could fine the new Area doing the following (I'm sure this approach is wrong):

.6 = pi*r^2, r*720 = 314.7
A = pi*314.7^2, plugging in the new area into T = IAB gives the wrong answer.

I'd be very grateful for any help.

 

[rl.bhat]

I got 1.32644e-8 N-m

 

[calvert11]

I got 1.32644e-8 N-m

yeah, Thanks. I got the same answer or thereabouts.

After some algebra (and some help) I found that the new area A2 = (n^2)*A1.

Plugging that into T = IAB gives the correct answer.