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A square loop of side 5 cm enters a magnetic field of flux density 0.4 T while travelling at a velocity of 6 m s^-1 parallel to one side of the square - Leaving Cert Physics - Question vi - 2021
Question vi
A square loop of side 5 cm enters a magnetic field of flux density 0.4 T while travelling at a velocity of 6 m s^-1 parallel to one side of the square. The square is... show full transcript
Worked Solution & Example Answer:A square loop of side 5 cm enters a magnetic field of flux density 0.4 T while travelling at a velocity of 6 m s^-1 parallel to one side of the square - Leaving Cert Physics - Question vi - 2021
Step 1
Use Faraday's law of electromagnetic induction to calculate the average emf induced in the loop as it enters the field.
Answer
Faraday's law states that the induced emf ( ( V ) ) in a circuit is equal to the rate of change of magnetic flux ( ( \Phi ) ). We start by calculating the area of the square loop:
$$A = s^2 = (0.05 \, m)^2 = 0.0025 \, m^2$$
Now we calculate the magnetic flux (
\( \Phi \)
):
$$\Phi = B * A = 0.4 \, T * 0.0025 \, m^2 = 0.001 \, Wb$$
The time (
\( t \)
) taken for the loop to fully enter the magnetic field can be calculated by the distance travelled divided by the velocity:
$$t = \frac{s}{v} = \frac{0.05 \, m}{6 \, m/s} = 0.00833 \, s$$
Applying Faraday's law, the average induced emf is:
$$V = \frac{d\Phi}{dt} = \frac{0.001 \, Wb}{0.00833 \, s} \approx 0.12 \, V$$
Step 2
Step 3
Explain how Lenz's law is a special case of the principle of conservation of energy.
Answer
Lenz's law reflects the principle of conservation of energy by ensuring that any induced current will always work to counteract the change in magnetic flux that produced it. If this were not the case, energy could be created from nothing, violating the conservation of energy principle. Thus, Lenz's law helps to maintain energy balance in electromagnetic systems.