Question

A coil of 10 turns is in the shape of an ellipse having a major axis of 13.0 cm and a minor axis of 6.00 cm. The coil rotates at 73rpm in a region in which the Earth's magnetic field is 55.0 microT. What is the maximum voltage induced in the coil if the axis of rotation of the coil is along its major axis and this axis of rotation is aligned perpendicular to the Earth's magnetic field

Answer 1

the maximum voltage induced in the coil is 2.574 × 10⁻⁵ V

Step-by-step explanation:

Given the data in the question;

Number of turns N = 10

major axis Ma = 13 cm = 0.13 m

a = 0.13/2 = 0.065 m

Minor axis Mi = 6 cm = 0.06 m

b = 0.06/2 = 0.03 m

we know that; 1 RPM = 0.10472 rad/s

rate of rotation R = 73rpm = 7.64 rad/s

Magnetic field = 55 uT

we know that, Area of ellipse = π × a × b

we substitute

A = π × 0.065 m × 0.03 m

A = 0.006126 m²

so

Maximum Voltage = N × Area × Magnetic field × rate of reaction

we substitute

Maximum Voltage = 10 × 0.006126 × ( 55 × 10⁻⁶ ) × 7.64

Maximum Voltage = 2.574 × 10⁻⁵ V

Therefore, the maximum voltage induced in the coil is 2.574 × 10⁻⁵ V