Question 3.1 [2 marks]
State Faraday's Law in words.
Faraday's Law states that the induced electromotive force (emf) in a closed circuit is directly proportional to the rate of change of magnetic flux through the circuit.
Question 3.2 [3 marks]
Calculate the change in magnetic flux.
To find the change in magnetic flux (\( \Delta \Phi \)), we use the formula:
\[ \text{emf} = -N \frac{\Delta \Phi}{\Delta t} \]
Where:
- \( N \) = number of windings = 500
- \( \Delta t \) = time taken to rotate = 0.09 s
- \(\text{emf} = 9 , \text{V}\)
Rearranging the formula to calculate the change in magnetic flux:
\[ \Delta \Phi = -\frac{\text{emf} \cdot \Delta t}{N} \]
Substituting the known values:
\[ \Delta \Phi = -\frac{9 , \text{V} \cdot 0.09 , \text{s}}{500} \]
\[ \Delta \Phi = -\frac{0.81 , \text{V}\cdot \text{s}}{500} = -0.00162 , \text{Wb} \]
Thus, the change in magnetic flux is \( \Delta \Phi = 0.00162 , \text{Wb} \) (we take the absolute value for the change).
Question 3.3 [4 marks]
Calculate the magnitude of the magnetic field.
The change in magnetic flux for the coil can also be expressed in terms of the area of the coil and the magnetic field (\( B \)). The area \( A \) of a square coil with a side length \( l \) is:
\[ A = l^2 \]
Given \( l = 4 , \text{cm} = 0.04 , \text{m} \):
\[ A = (0.04 , \text{m})^2 = 0.0016 , \text{m}^2 \]
Now we can relate the change in magnetic flux to the magnetic field as follows:
\[ \Delta \Phi = B \cdot A \cdot \cos(\theta) \]
Where:
- \( \theta \) = change in angle = \( 45^\circ \)
Since the coil is initially perpendicular to the magnetic field (so \( \cos(0) = 1 \)) and at the final position, it's at an angle of 45° (so \( \cos(45) = \frac{1}{\sqrt{2}} \)), we have:
\[ \Delta \Phi = B \cdot A \cdot \left(\cos(0) - \cos(45)\right) = B \cdot A \cdot \left(1 - \frac{1}{\sqrt{2}}\right) \]
Now substituting \( \Delta \Phi \) and \( A \):
\[ 0.00162 = B \cdot 0.0016 \cdot \left(1 - \frac{1}{\sqrt{2}}\right) \]
Calculating \( (1 - \frac{1}{\sqrt{2}}) \):
\[ 1 - \frac{1}{\sqrt{2}} \approx 1 - 0.7071 \approx 0.2929 \]
Thus:
\[ 0.00162 = B \cdot 0.0016 \cdot 0.2929 \]
Solving for \( B \):
\[ B = \frac{0.00162}{0.0016 \cdot 0.2929} \approx \frac{0.00162}{0.000467 \approx 3.46 , \text{T} \]
Question 3.4 [2 marks]
If the time taken to rotate the coil decreased to 0.04s, how would this affect the emf value? Write only INCREASES, DECREASES or STAYS THE SAME. Explain your answer.
INCREASES
Explanation: According to Faraday's Law, the induced emf is proportional to the rate of change of magnetic flux. If the time taken to rotate the coil decreases, the rate of change of magnetic flux increases, which results in a higher induced emf.
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