Final answer:
Faraday's law states that an emf is induced when there is a change in magnetic flux through a coil. The induced emf in a coil with 200 windings as the magnetic flux changes is -400 V. The magnitude of the induced emf can be increased by adding more turns to the coil or by increasing the rate of change of the magnetic flux.
Step-by-step explanation:
Faraday's law of electromagnetic induction states that an electromotive force (emf) is induced in a coil when there is a change in magnetic flux through the coil. To calculate the induced emf in a coil with 200 windings when the magnetic flux linkage with each winding changes from 1 x 10-4 Wb to 5 x 10-4 Wb in 0.2 seconds, we use the formula:
E = -N(\Delta\Phi / \Delta t)
where:
- E is the induced emf,
- N is the number of turns (windings) in the coil,
- \(\Delta\Phi\) is the change in magnetic flux,
- \(\Delta t\) is the time over which the change occurs.
First, calculate the change in flux (\(\Delta\Phi\)):
\(\Delta\Phi = \Phi_{final} - \Phi_{initial} = 5 x 10^{-4} - 1 x 10^{-4} = 4 x 10^{-4} Wb\).
Then, plug into the formula:
E = -200 * (4 x 10-4 / 0.2) = -400 V (the negative sign indicates the direction of the induced emf, as per Lenz's law).
As the flux linkage has increased, this suggests the coil was rotated to an angle closer to 90° relative to the magnetic field, maximising the component of the magnetic field perpendicular to the coil and hence increasing the flux linkage.
To increase the magnitude of the induced emf, one could:
- Increase the number of turns in the coil.
- Increase the rate at which the magnetic flux changes through the coil.