The question provided in the image asks about a coil of wire with 2000 turns, a cross-sectional area of $6.9 \times 10^{-6} \, \text{m}^2$, and a uniform magnetic field strength of $8.0 \times 10^{-4} \, \text{T}$. It further asks for:

1. The calculation of the maximum electromotive force (EMF).
2. The calculation of the magnetic flux.

Let's solve both questions step by step.

1. Magnetic Flux ($\Phi_B$)

The magnetic flux through the coil is given by: $\Phi_B = B \cdot A \cdot \cos \theta$ Where:

• $B = 8.0 \times 10^{-4} \, \text{T}$ (magnetic field strength),
• $A = 6.9 \times 10^{-6} \, \text{m}^2$ (cross-sectional area),
• $\theta = 0^\circ$ since the magnetic field is perpendicular to the plane of the coil ($\cos 0^\circ = 1$).

Substituting: $\Phi_B = (8.0 \times 10^{-4}) \cdot (6.9 \times 10^{-6}) \cdot 1$ $\Phi_B = 5.52 \times 10^{-9} \, \text{Wb (Weber)}.$

2. Maximum EMF ($\mathcal{E}_{\text{max}}$)

The maximum induced EMF in a coil is given by Faraday's law of induction: $\mathcal{E}_{\text{max}} = N \cdot \frac{d\Phi_B}{dt}$ Where:

• $N = 2000$ (number of turns),
• $\frac{d\Phi_B}{dt}$ is the rate of change of the magnetic flux. For maximum EMF, the flux changes from $+\Phi_B$ to $-\Phi_B$ in half a cycle.

If the magnetic flux alternates sinusoidally at a frequency $f$, the rate of change of flux is: $\frac{d\Phi_B}{dt} = 2 \pi f \Phi_B$

However, the frequency $f$ is not given in the question. To calculate the exact value, we would need the frequency of the changing field. If a specific value for $f$ is provided, substitute it into the formula: $\mathcal{E}_{\text{max}} = N \cdot 2 \pi f \Phi_B$

For now, the formula remains: $\mathcal{E}_{\text{max}} = 2000 \cdot 2 \pi f \cdot (5.52 \times 10^{-9})$

You can plug in the frequency $f$ to get the numerical result for maximum EMF.

Would you like clarification or additional details about the above calculations? Here are some related questions to consider:

1. What happens to the magnetic flux if the angle $\theta$ changes?
2. How is the EMF affected if the magnetic field $B$ varies with time?
3. What is the role of frequency in determining the maximum EMF in a coil?
4. How would the results change if the coil had fewer turns (e.g., 1000 instead of 2000)?
5. How can you experimentally measure the magnetic flux in such a coil?

Tip: Always ensure that all quantities are in their standard SI units before substituting into formulas for accurate results.