Answer:
B. 5.0 V
Explanation:
The induced electromotive force (emf) in a coil is given by Faraday's law of electromagnetic induction, which states that the induced emf [tex](\( \varepsilon \))[/tex] is equal to the rate of change of magnetic flux [tex](\( \Phi \))[/tex] through the coil.
The formula for Faraday's law is:
[tex]\[ \varepsilon = -N \frac{\Delta \Phi}{\Delta t} \][/tex]
Where:
- [tex]\( \varepsilon \)[/tex]mf, is the induced emf
[tex]- \( N \)[/tex] is the number of turns (loops) in the coil,
[tex]- \( \Delta \Phi \)[/tex] is the change in magnetic flux,
[tex]- \( \Delta t \)[/tex] is the change in time.
The magnetic flux [tex](\( \Phi \))[/tex] is given by the product of the magnetic field (\( B \)), the area [tex](\( A \))[/tex] through which the magnetic field lines pass, and the cosine of the angle [tex](\( \theta \))[/tex] between the magnetic field lines and the normal to the area:
[tex]\[ \Phi = B \cdot A \cdot \cos(\theta) \][/tex]
In this case, the coil is placed normally to the magnetic field, so [tex]\( \theta = 0° \) and \( \cos(0°) = 1 \).[/tex] Therefore, the formula simplifies to:
[tex]\[ \Phi = B \cdot A \][/tex]
Given that:
[tex]- \( B = 1 \, \text{T} \) (the magnetic field increases at a rate of \( 1 \, \text{T/s} \)),[/tex]
- \( A = 500 \) square loops, each of side \( 10 \, \text{cm} \) (\( A = 500 \times (0.1 \, \text{m})^2 \)),
[tex]- \( \Delta t = 1 \, \text{s} \) (the change in time is \( 1 \, \text{s} \)).[/tex]
Now, substitute these values into the formula for induced emf:
[tex]\[ \varepsilon = -N \frac{\Delta \Phi}{\Delta t} \][/tex]
[tex]\[ \varepsilon = -500 \frac{(1 \, \text{T} \cdot 500 \times (0.1 \, \text{m})^2)}{1 \, \text{s}} \][/tex]
[tex]\[ \varepsilon = -500 \times (0.1)^2 \, \text{V} \][/tex]
[tex]\[ \varepsilon = -5 \times 10^{-3} \, \text{V} \][/tex]
The negative sign indicates the direction of the induced emf. However, since the question is asking for the magnitude, the answer is:
[tex]\[ \text{Induced emf} = 5 \times 10^{-3} \, \text{V} \][/tex]
So, the correct answer is:
[tex]\[ \text{B. } 5.0 \, \text{V} \][/tex]
