A wire is formed into a circle having a diameter of 19.0 cm and placed in a uniform magnetic field of 3.40 mT. The wire carries a current of 5.00 A. (a) Find the maximum torque on the wire. µN · m (b) Find the range of potential energies of the wire-field system for different orientations of the circle. minimum µJ maximum µJ

Radius = 9.5 x 10⁻² m

area of circle = 3.14 x (9.5 x 10⁻²) ²

A = 283.38 x 10⁻⁴ m²

magnetic moment = area x current

M = 283.38 x 10⁻⁴ x 5

= 1416.9 x 10⁻⁴ Am²

Torque = MBsinθ

M is magnetic moment, B is magnetic field.

Max torque = 1416.9 x 10⁻⁴ x 3.4 x 10⁻³, for θ = 90

= 4817.46 x 10⁻⁷

= 481.7 x 10⁻⁶

= 481.7 μ J

Energy = - MBcosθ

Max energy when θ = 180

MB = 4817.46 x 10⁻⁷ J

Min energy = - 4817.46 x 10⁻⁷ for θ = 0