A magnet is plunged into and out of a coil of wire 2 times per second. This induces 5 volts.
a- If the rate of motion changes so that the magnet is plunged in and out 6 times per second, what will be the new induced voltage?
b- if the number of coils in the wire is doubled from 100 to 200 , and the original rate of 2 times per second is kept the same, what will be the new voltage induced?
To answer these questions, we need to understand the relationship between the rate of motion of a magnet in and out of a coil of wire and the induced voltage. The key concept here is Faraday's Law of Electromagnetic Induction, which states that the induced voltage (emf) in a wire coil is proportional to the rate at which the magnetic field passing through the coil changes.
a- If the rate of motion changes so that the magnet is plunged in and out 6 times per second, we can use the concept of proportionality from Faraday's Law to find the new induced voltage. Since the rate of motion is now three times the original rate, we can expect the induced voltage to be three times the original voltage.
Therefore, the new induced voltage would be 3 times 5 volts, which equals 15 volts.
b- If the number of coils in the wire is doubled from 100 to 200, while keeping the original rate of 2 times per second, we can again use Faraday's Law to determine the new induced voltage. According to the law, the induced voltage is directly proportional to the number of coils.
Since the number of coils has doubled, we can expect the induced voltage to also double. Therefore, the new induced voltage would be 2 times the original voltage of 5 volts, which equals 10 volts.
In both cases, it's important to note that these explanations are based on the assumption that all other factors remain constant, such as the magnetic field strength and the area of the wire coil.