Question

If a coil of wire in a magnetic field rotates 60 degrees, it provides an emf averaging 0.17 v . if the coil consists of 3 loops of radius 0.50 m and the magnetic field has a strength of 9.0 mt , how long does it take the coil to complete its rotation? assume the coil is initially facing perpendicular to the field. express your answer with the appropriate units. activate to select the appropriates template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices.

Answer 1

In this case, it takes approximately 0.411 seconds for the coil to complete its rotation.

Step-by-step explanation:

To find the time it takes for the coil to complete its rotation, we can use the concept of angular velocity.

1. Convert the rotation angle from degrees to radians:

The given rotation angle is 60 degrees. To convert it to radians, we use the formula:

• Angle in radians = (Angle in degrees * π) / 180
• Angle in radians = (60 degrees * π) / 180 = π/3 radians

2. Calculate the average induced emf:

The average induced emf can be found using Faraday's law of electromagnetic induction:

Average induced emf (ε) = -N * ΔΦ / Δt

where N is the number of loops in the coil, ΔΦ is the change in magnetic flux, and Δt is the change in time.

Given:

• Average induced emf (ε) = 0.17 V
• Number of loops in the coil (N) = 3

Since the coil consists of 3 loops and the emf is averaged, the total induced emf is 3 times the average emf:

Total induced emf (ε-total) = N * ε = 3 * 0.17 V = 0.51 V

3. Calculate the change in magnetic flux:

The change in magnetic flux can be found using the formula:

Change in magnetic flux (ΔΦ) = B * A * Δθ

where B is the magnetic field strength, A is the area of the coil, and Δθ is the change in angle.

Given:

• Magnetic field strength (B) = 9.0 mT = 9.0 * 10⁻³ T
• Radius of the coil (r) = 0.50 m
• Change in angle (Δθ) = π/3 radians

The area of each loop in the coil is given by:

• Area of each loop (A) = π * r²
• Area of each loop (A) = π * (0.50 m)² = 0.785 m²

The total change in magnetic flux is the change in flux for each loop multiplied by the number of loops:

• Total change in magnetic flux (ΔΦ) = N * B * A * Δθ
• Total change in magnetic flux (ΔΦ) = 3 * (9.0 * 10^(-3) T) * (0.785 m²) * (π/3 radians) ≈ 0.0703 Tm²

4. Calculate the time to complete the rotation:

We can rearrange Faraday's law to solve for the change in time:

Δt = -N * ΔΦ / ε-total

Given:

• Number of loops in the coil (N) = 3
• Total change in magnetic flux (ΔΦ) ≈ 0.0703 Tm²
• Total induced emf (ε-total) = 0.51 V

Substituting the values into the equation, we find:

Δt = -3 * (0.0703 Tm²) / (0.51 V) ≈ -0.411 s

Since time cannot be negative, we take the absolute value:

Δt ≈ 0.411 s

Therefore, it takes approximately 0.411 seconds for the coil to complete its rotation.