To calculate the electromagnetic parameters for the coil, we'll use Faraday's law of electromagnetic induction, which states that the induced emf (voltage) in a coil is given by the rate of change of magnetic flux through the coil. Here are the steps to determine both the maximum emf and the instantaneous emf after a certain rotation.
### Given Data
- Number of turns (\( N \)): 450 turns
- Mean length per turn: 25 cm (or 0.25 meters)
- Speed of the coil: 18 m/s
- Magnetic flux density (\( B \)): 0.011 Tesla
### A) Maximum emf Induced in the Coil
First, we need the area of the coil to calculate the magnetic flux.
#### Step-by-Step Calculation:
1. **Calculate the area (\( A \)) of the coil per turn:**
Given the mean length per turn is 25 cm (0.25 meters), assume the coil forms a circular loop. The circumference \( C \) is 0.25 meters, so:
\[
C = 2\pi r \implies r = \frac{C}{2\pi} = \frac{0.25}{2\pi} \approx 0.0398 \text{ meters}
\]
Thus, the area \( A \) of one turn is:
\[
A = \pi r^2 = \pi (0.0398)^2 \approx 4.98 \times 10^{-3} \text{ square meters}
\]
2. **Calculate the maximum induced emf:**
The maximum emf (\( \mathcal{E}_{max} \)) is given by:
\[
\mathcal{E}_{max} = NBA\omega
\]
where \( \omega \) is the angular velocity of the coil in radians per second.
3. **Determine the angular velocity (\( \omega \)):**
Since the linear speed \( v = 18 \) m/s and the radius \( r \approx 0.0398 \) m:
\[
\omega = \frac{v}{r} = \frac{18}{0.0398} \approx 452.26 \text{ radians/second}
\]
4. **Substitute the values into the emf equation:**
\[
\mathcal{E}_{max} = 450 \times 0.011 \times 4.98 \times 10^{-3} \times 452.26
\]
\[
\mathcal{E}_{max} \approx 11.1 \text{ volts}
\]
### B) Instantaneous Value of the emf after 30° of Revolution
The instantaneous emf (\( \mathcal{E}(t) \)) at any angle \( \theta \) is given by:
\[
\mathcal{E}(t) = \mathcal{E}_{max} \sin(\theta)
\]
where \( \theta \) is the angular position in radians. After 30 degrees of revolution:
\[
\theta = 30^\circ = \frac{\pi}{6} \text{ radians}
\]
So, substitute \( \theta \):
\[
\mathcal{E}(30^\circ) = \mathcal{E}_{max} \sin\left(\frac{\pi}{6}\right) = 11.1 \times \sin\left(\frac{\pi}{6}\right) = 11.1 \times 0.5 = 5.55 \text{ volts}
\]
### Summary:
- **Maximum emf induced in the coil:** \( \approx 11.1 \text{ volts} \)
- **Instantaneous emf after 30° of revolution:** \( \approx 5.55 \text{ volts} \)
A coil of 450turns with a mean length per turn of 25cm, rotates at 18m/s in a magnetic field that has a magnetic flux density of 0,011 tesla. Calculate
A) maximum emf induced in the coil
B) instantaneous value of the emf after 30° of revolution
1 answer