Question

Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field acting perpendicularly to its axis of rotation. Coil 1 has a radius of 4.8 cm and rotates in a 0.15-T field. Coil 2 rotates in a 0.32-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2?

Answer 1

$$\tau_a=\tau_b\\N _o B _a I_ o A_ a = N_ o B_ b I_ o A_ b$$

$$B_ a A_ a = B _b A_ b \\ \pi B_aR_a^2=\pi B_bR_b^2\\$$

$$(0.15)(4.8)^2=(0.32)R_b^2\\R_b=3.29\ cm$$