# Faraday’s Law and Lenz's Law Electromagnetic Induction Simulation

#### Quiz

A. an emf is induced in a loop when it moves through an electric field
B. the induced emf produces a current whose magnetic field opposes the original change
C. the induced emf is proportional to the rate of change of magnetic flux

Q2)  If a coil is shrinking in a B field pointing into the page, in what direction is the induced current?

A. clockwise
B. counter-clockwise
C. no induced current

Downward flux is decreasing, so need to create downward B field.

#### Faraday’s Law Electromagnetic Induction Simulation(Virtual Experiment)

When the next simulation is not visible, please refer to the following link.

Faraday and Henry both made the same discovery. Electric current can be produced in a wire by simply moving a magnet into or out of a wire coil. No battery or other voltage source was needed only the motion of a magnet in a coil or in a single wire loop as shown in Figure 1.

FIGURE 1. When the magnet is plunged into the coil, voltage is induced in the coil and charges in the coil are set in motion.

They discovered that voltage was induced by the relative motion of a wire with respect to a magnetic field. The production of voltage depends only on the relative motion of the conductor with respect to the magnetic field. Voltage is induced whether the magnetic field of a magnet moves past a stationary conductor, or the conductor moves through a stationary magnetic field as shown in Figure 2. The results are the same for the same relative motion.

FIGURE 2. Voltage is induced in the wire loop whether the magnetic field moves past the wire or the wire moves through the magnetic field.

To see how an emf can be induced by a changing magnetic field, consider a loop of wire connected to a sensitive ammeter, as illustrated in Figure 3. When a magnet is moved toward the loop, the galvanometer needle deflects in one direction, arbitrarily shown to the right in Figure 3a. When the magnet is brought to rest and held stationary relative to the loop (Fig. 3b), no deflection is observed. When the magnet is moved away from the loop, the needle deflects in the opposite direction, as shown in Figure 3c. Finally, if the magnet is held stationary and the loop is moved either toward or away from it, the needle deflects. From these observations, we conclude that the loop detects that the magnet is moving relative to it and we relate this detection to a change in magnetic field. Thus, it seems that a relationship exists between current and changing magnetic field.
These results are quite remarkable in view of the fact that a current is set up even though no batteries are present in the circuit! We call such a current an induced current and say that it is produced by an induced emf.

Figure 3 (a) When a magnet is moved toward a loop of wire connected to a sensitive ammeter, the ammeter deflects as shown, indicating that a current is induced in the loop. (b) When the magnet is held stationary, there is no induced current in the loop, even when the magnet is inside the loop. (c) When the magnet is moved away from the loop, the ammeter deflects in the opposite direction, indicating that the induced current is opposite that shown in part (a). Changing the direction of the magnet’s motion changes the direction of the current induced by that motion.

Now let us describe an experiment conducted by Faraday and illustrated in Figure 4. A primary coil is connected to a switch and a battery. The coil is wrapped around an iron ring, and a current in the coil produces a magnetic field when the switch is closed. A secondary coil also is wrapped around the ring and is connected to a sensitive ammeter. No battery is present in the secondary circuit, and the secondary coil is not electrically connected to the primary coil. Any current detected in the secondary circuit must be induced by some external agent.

Initially, you might guess that no current is ever detected in the secondary circuit. However, something quite amazing happens when the switch in the primary circuit is either opened or thrown closed. At the instant the switch is closed, the galvanometer needle deflects in one direction and then returns to zero. At the instant the switch is opened, the needle deflects in the opposite direction and again returns to zero.

Figure 4. Faraday’s experiment. When the switch in the primary circuit is closed, the ammeter in the secondary circuit deflects momentarily. The emf induced in the secondary circuit is caused by the changing magnetic field through the secondary coil.

Finally, the galvanometer reads zero when there is either a steady current or no current in the primary circuit. The key to understanding what happens in this experiment is to first note that when the switch is closed, the current in the primary circuit produces a magnetic field in the region of the circuit, and it is this magnetic field that penetrates the secondary circuit. Furthermore, when the switch is closed, the magnetic field produced by the current in the primary circuit changes from zero to some value over some finite time, and this changing field induces a current in the secondary circuit.

As a result of these observations, Faraday concluded that an electric current can be induced in a circuit (the secondary circuit in our setup) by a changing magnetic field. The induced current exists for only a short time while the magnetic field through the secondary coil is changing. Once the magnetic field reaches a steady value, the current in the secondary coil disappears. In effect, the secondary circuit behaves as though a source of emf were connected to it for a short time. It is customary to say that an induced emf is produced in the secondary circuit by the changing magnetic field.
The experiments shown in Figures 3 and 4 have one thing in common: in each case, an emf is induced in the circuit when the magnetic flux through the circuit changes with time. In general,

The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit.

This statement, known as Faraday’s law of electromagnetic induction, can be written

 Faraday’s Law $\ E = -N \frac {d\Phi_{B}}{dt}$ where $\Phi_{B} =\int \mathbf{B}\cdot d\mathbf{A}$ is the magnetic flux through the circuit in N loops.

Lenz’s Law
The SI unit for the induced emf is the volt, V. The minus sign in the above Faraday’s law of induction is due to the fact that the induced emf will always oppose the change. It is also known as the Lenz’s law and it is stated as follows,

 Lenz’s Law The current from the induced emf will produce a magnetic field, which will always oppose the original change in the magnetic flux.