Earth’s magnetic field question

Question

The orientation of small satellites is often controlled using toque from current-carrying coils in Earth’s magnetic field. Suppose a multiturn coil has a cross-sectional area of 6.36 × 10^-4 m², dissipates 0.200 W of electrical power from a 5.00 V power supply, and provides a magnetic moment of magnitude 0.0200 A•m².

(a) Find the coil current I.

(b) Calculate the maximum magnitude of torque if Earth’s magnetic field has magnitude 3.75 × 10^-5 T at the satellite’s location.

Answer 1

a) You can use the power equation

P = IV ⇒ I = P/V = 0.2 W / 5.00 V = 40 mA

b) For this you can use the torque magnitude equation, where μ magnetic moment magnitude, B is the magnetic field magnitude, and θ is the angle between the vectors. (this equations is uncommon and I forget it exists all the time) Also remember that sinθ ≤ 1.

T = μ B sinθ ≤ (0.02 A m² )( 3.75 × 10^-5 T) = 7.5 × 10^-7 Nm