Faraday's law: If the number of loops in a coil around a moving magnet doubles what happens to the brightness of the bulb if the speed of the magnet remains the same?
Faraday's law of electromagnetic induction states that a changing magnetic field induces an electromotive force (EMF) in a closed circuit. This induced EMF results in a current flow, which can power devices such as a light bulb.
In this scenario, you stated that the number of loops in a coil around a moving magnet doubles while the speed of the magnet remains the same. Let's analyze the impact on the brightness of the bulb.
According to Faraday's law, the induced EMF is directly proportional to the rate of change of the magnetic flux through the coil. The magnetic flux depends on two factors: the strength of the magnetic field and the area of the coil that the field lines cross.
When the number of loops in the coil doubles, the area of the coil that the field lines cross also doubles. This means that the magnetic flux through the coil will increase by a factor of two.
Assuming the speed of the magnet remains the same, the rate of change of the magnetic flux remains constant. Since the induced EMF is directly proportional to the rate of change of the magnetic flux, it will also double.
The brightness of the bulb is directly related to the current flowing through it. The induced EMF drives the current, and if the induced EMF doubles, the current flowing through the bulb will also double.
As a result, if the number of loops in the coil around a moving magnet doubles while the speed of the magnet remains the same, the brightness of the bulb will also double.
To summarize:
- Increasing the number of loops in the coil around a moving magnet doubles the area of the coil that the magnetic field lines cross.
- This, in turn, doubles the magnetic flux through the coil.
- The induced electromotive force (EMF) is directly proportional to the rate of change of the magnetic flux.
- If the speed of the magnet remains the same, the rate of change of the magnetic flux remains constant.
- Therefore, the induced EMF will double, resulting in double the current flowing through the bulb.
- Double the current means double the brightness of the bulb.