To solve this problem, we need to use Faraday's law of electromagnetic induction, which states that the induced voltage in a loop is equal to the rate of change of the magnetic flux through the loop.

The formula for Faraday's law is:

V = -dΦ/dt

Where:
V is the induced voltage,
dΦ/dt is the rate of change of the magnetic flux.

The magnetic flux (Φ) through a loop is given by the formula:

Φ = BAcosθ

Where:
B is the magnetic field strength,
A is the area of the loop,
θ is the angle between the magnetic field and the normal to the loop.

In this case, since the ring is spinning, the angle θ is constantly changing. However, the maximum induced voltage occurs when θ = 90 degrees, because that's when the rate of change of the magnetic flux is greatest. At this point, cosθ = 0, so the magnetic flux is zero, and the induced voltage is at its maximum.

So, we can write Faraday's law as:

Vmax = -d(0)/dt = -dB/dt * A

Where:
dB/dt is the rate of change of the magnetic field strength,
A is the area of the loop.

We know that the maximum induced voltage Vmax = 1.656E-6 V, and the magnetic field strength B = 4.490⋅10−5 T. We also know that the ring is spinning at a rate of 18.50 rotations per second, so the rate of change of the magnetic field strength dB/dt = 18.50 * B.

Substituting these values into the equation gives:

1.656E-6 V = -18.50 * 4.490⋅10−5 T * A

Solving for A gives:

A = 1.656E-6 V / (-18.50 * 4.490⋅10−5 T) = 0.00198 m^2

The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. Since the rotation axis is the diameter of the ring, the radius r is half the diameter. So, we can write the area as A = π(D/2)^2, where D is the diameter of the ring.

Substituting A = 0.00198 m^2 into this equation and solving for D gives:

0.00198 m^2 = π(D/2)^2

D = 2 * sqrt(0.00198 m^2 / π) = 0.0502 m = 5.02 cm

So, the diameter of the ring is approximately 5.02 cm.

Question

To solve this problem, we need to use Faraday's law of electromagnetic induction, which states that the induced voltage in a loop is equal to the rate of change of the magnetic flux through the loop.

The formula for Faraday's law is:

V = -dΦ/dt

Where:
V is the induced voltage,
dΦ/dt is the rate of change of the magnetic flux.

The magnetic flux (Φ) through a loop is given by the formula:

Φ = BAcosθ

Where:
B is the magnetic field strength,
A is the area of the loop,
θ is the angle between the magnetic field and the normal to the loop.

In this case, since the ring is spinning, the angle θ is constantly changing. However, the maximum induced voltage occurs when θ = 90 degrees, because that's when the rate of change of the magnetic flux is greatest. At this point, cosθ = 0, so the magnetic flux is zero, and the induced voltage is at its maximum.

So, we can write Faraday's law as:

Vmax = -d(0)/dt = -dB/dt * A

Where:
dB/dt is the rate of change of the magnetic field strength,
A is the area of the loop.

We know that the maximum induced voltage Vmax = 1.656E-6 V, and the magnetic field strength B = 4.490⋅10−5 T. We also know that the ring is spinning at a rate of 18.50 rotations per second, so the rate of change of the magnetic field strength dB/dt = 18.50 * B.

Substituting these values into the equation gives:

1.656E-6 V = -18.50 * 4.490⋅10−5 T * A

Solving for A gives:

A = 1.656E-6 V / (-18.50 * 4.490⋅10−5 T) = 0.00198 m^2

The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. Since the rotation axis is the diameter of the ring, the radius r is half the diameter. So, we can write the area as A = π(D/2)^2, where D is the diameter of the ring.

Substituting A = 0.00198 m^2 into this equation and solving for D gives:

0.00198 m^2 = π(D/2)^2

D = 2 * sqrt(0.00198 m^2 / π) = 0.0502 m = 5.02 cm

So, the diameter of the ring is approximately 5.02 cm.

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