Question

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. (Figure 1)

Part A

If the speed of the magnet is doubled, the induced voltage is ________.

a.) twice as great

b.) four times as great

c.) half as great

d.) unchanged

 

Answer 1

Concepts and reason The concepts used to solve this problem are electromagnetic induction by a moving magnet and Faraday's law. Use the factors that depend on the electromagnetic induction of a moving magnet to find the correct option.

Fundamentals

"Faraday's law of induction states that whenever relative motion exists between a coil and magnetic field, a voltage will induce in the circuit and this voltage is proportional to the rate of change of the flux." The quick change in the flux will induce more emf than a gradual change. The expression for the motional emf is as follows:

\(\varepsilon=B l v\)

Here, \(\varepsilon\) is the motional emf, \(B\) is the magnetic field, \(l\) is the length of the conductor, and \(v\) is the velocity at which the magnetic field changes.

(A) The incorrect options are given below:

b) Four times as great

c) Half as great

d) Unchanged The expression for the motional emf is as follows:

\(\varepsilon=B l v\)

The induced voltage by the moving magnet is directly proportional to the speed of the magnet. Therefore, an increase in the speed of the magnet will increase the induced voltage.

Explanation | Common mistakes | Hint for next step

The magnitude of the electromagnetic induction is equal to the product of flux density, length of the conductor, and the velocity of motion.

Step 2 of 2

The correct option is given below:

b) Twice as great The expression for the motional emf is as follows:

\(\varepsilon=B l v\)

The magnitude of the induced voltage is proportional to the speed of the motion. Therefore, as the speed of the magnet is doubled, the induced voltage will be doubled. This is because the current will have to be twice as fast to keep up. Ohm's law:

\(V=I R\)

Here, \(\mathrm{V}\) is the potential difference, \(\mathrm{l}\) is the current, and \(\mathrm{R}\) is the resistance. If the resistance is constant, then the voltage must also be doubled.

An increase in the speed of the magnet will increase the induced voltage. Therefore, when the speed of the magnet is doubled, the induced voltage will also get doubled.

Part \(\mathrm{A}\) The induced voltage is twice, as the speed of the magnet is doubled.