Question

A single loop of wire with a radius of 7.5 cm rotates about a diameter in a uniform magnetic field of 1.6T. To produce a maximum emf of 1.0V, it should rotate at:

a.0
b.2.7 rad/s
c.5.6 rad/s
d.35 rad/s
e.71 rad/s

Answer 1

Using Faraday's law of electromagnetic induction, we calculate the angular velocity needed for a single wire loop of radius 7.5 cm to generate a maximum emf of 1.0V in a 1.6T magnetic field.

Step-by-step explanation:

To determine the angular velocity at which the single loop of wire should rotate to produce a maximum emf of 1.0V in a magnetic field of 1.6T, we can use Faraday's law of electromagnetic induction. The emf (E) induced in a rotating loop is given by E = NABωsin(ωt), where N is the number of turns (which is 1 for a single loop), A is the area of the loop, B is the magnetic field strength, ω is the angular velocity, and ωt is the angle between the field and normal to the loop (which is π/2 radians for maximum emf).

For a single loop, E = AωB. The area (A) of the loop can be calculated using the formula for the area of a circle, A = πr2, where r is the radius. Substituting in the given values (r = 0.075 m, B = 1.6T, and E = 1.0V), the equation becomes 1.0V = π(0.075 m)2(1.6T)ω. Solving for ω gives us an angular velocity that the loop must rotate at to produce the specified emf.