Question

A merry-go-round has an area of 300 m2 and spins at 2rpm about a vertical axis at a place where the Earth's magneticfield is vertical and has a magnitude of 5x10-5 T. The emf around the rim is:

A. 0
B. .5mV
C. 3.1mV
D. 15mV
E. 30mV

Answer 1

The induced emf in a merry-go-round rotating in a vertical magnetic field is 3.1 mV, calculated using Faraday's law with the given magnetic field strength, area, and angular velocity.

Step-by-step explanation:

The question is asking for the electromotive force (emf) induced in a merry-go-round as it spins in a magnetic field. The emf generated around the rim of a spinning disc (the merry-go-round) in a magnetic field can be calculated using Faraday's law of electromagnetic induction. The relevant formula for calculating the induced emf (E) is E = B*A*ω, where B is the magnetic field strength, A is the area of the disc, and ω is the angular velocity in radians per second. The area is given as 300 m² and the spin rate is 2 rotations per minute (rpm), which we must convert to radians per second.

First, convert rpm to radians per second: 2 rpm * (2π radians/1 rotation) * (1 min/60 seconds) = 0.2094 radians/second. Now using the formula to find the induced emf: E = 5 x 10-5 T * 300 m2 * 0.2094 radians/second = 0.03138, or approximately 3.1 mV. Therefore, the answer is C. 3.1mV.