To determine the flux density of the magnetic field required to generate a voltage of 12.6 V in a conductor, we can use the formula for the induced electromotive force (EMF) in a moving conductor:

$\text{EMF} = B \cdot L \cdot v \cdot \sin(\theta)$

Where:

• $\text{EMF} = 12.6 \, \text{V}$
• $B$ is the magnetic flux density (in teslas, T) that we need to find.
• $L = 2 \, \text{m}$ is the effective length of the conductor.
• $v = 10.5 \, \text{m/s}$ is the velocity of the conductor.
• $\theta = 90^\circ$ is the angle between the velocity and the magnetic field.

Since $\theta = 90^\circ$, $\sin(\theta) = 1$. The equation simplifies to:

$\text{EMF} = B \cdot L \cdot v$

Now, we solve for $B$:

$B = \frac{\text{EMF}}{L \cdot v}$

Substituting the given values:

$B = \frac{12.6 \, \text{V}}{2 \, \text{m} \cdot 10.5 \, \text{m/s}}$

$B = \frac{12.6}{21} \, \text{T}$

$B = 0.6 \, \text{T}$

So, the flux density $B$ required is 0.6 T (teslas).

---

Would you like further details or have any questions? Here are some related questions:

1. What happens to the induced voltage if the velocity of the conductor increases?
2. How would the flux density change if the angle between the conductor's velocity and the magnetic field was different?
3. What is the effect of increasing the length of the conductor on the induced EMF?
4. How would the calculation change if the magnetic field was not uniform?
5. What is the physical interpretation of magnetic flux density?

Tip: When dealing with electromagnetic induction, always check the angle between the conductor's movement and the magnetic field, as it can significantly affect the induced EMF.