The induced electromotive force (emf) in a loop is given by Faraday's Law of Induction:

$\text{emf} = -\frac{\Delta \Phi_B}{\Delta t}$

where:

• $\Delta \Phi_B = \Delta B \cdot A$ is the change in magnetic flux,
• $A = 0.8 \, \text{m}^2$ is the area of the loop,
• $\Delta B$ is the change in magnetic field,
• $\Delta t = 3.6 \, \text{s}$ is the time over which the change occurs,
• $\text{emf} = 3.7 \, \text{V}$ is the induced emf.

Step 1: Rearrange Faraday's Law to find $\Delta B$:

$\text{emf} = -\frac{\Delta B \cdot A}{\Delta t}$ Taking the magnitude: $\Delta B = \frac{\text{emf} \cdot \Delta t}{A}$

Step 2: Substitute the given values:

$\Delta B = \frac{3.7 \cdot 3.6}{0.8}$

Step 3: Calculate:

$\Delta B = \frac{13.32}{0.8} = 16.65 \, \text{T}$

Final Answer:

$\Delta B = 16.7 \, \text{T}$

Let me know if you would like further clarifications!

Related Questions:

1. What factors affect the induced emf in a loop of wire?
2. How would the result change if the area of the loop were doubled?
3. What role does the time of induction play in determining the change in the magnetic field?
4. Can this principle be applied in designing electrical generators? How?
5. What would the induced emf be if the magnetic field changed in 1.8 seconds instead of 3.6 seconds?

Tip:

Always ensure that units are consistent (e.g., area in square meters, time in seconds) when applying Faraday's Law.