## Mastering Physics Solutions: A Magnet and a Coil

A Magnet and a Coil

Part A = twice as great
Part B = unchanged

Solutions Below:

When a magnet is plunged into a coil at speed v, as shown in the figure, a voltage is induced in the
coil and a current flows in the circuit.

Part A

If the speed of the magnet is doubled, the induced voltage is?

Since current is just the amount of charge movement per unit time, if the magnet moves twice as fast, then the current will have to be twice as fast to keep up. Since V = IR, if the resistance is constant, then the voltage must also double.

twice as great

Part B

The same magnet is plunged into a coil that has twice the number of turns as before. The magent
is shown before it enters the coil in the figure. If the speed of the magnet is again , the induced
current in the coil is?

By increasing the number of turns in the coil, the induced emf increases, but so does the
resistance of the coil. Since those two quantities increase by the same factor, their ratio
remains constant, and the induced current in the circuit is unchanged.

unchanged

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