Lenz’s Law and Faraday’s Law

Michael Faraday

Faraday’s Discovery A changing magnetic flux through a loop of wire causes an induced current in the wire.

Any induced current in a loop of wire will also have an induced magnetic field associated with it. In order to determine the direction of the induced B field in the center of the loop, we can use RHR #3!

Right-Hand Rule #3 If you wrap your fingers around like the current in a loop of wire, your thumb will show the direction of the magnetic field in the center of the loop caused by that current! I B

Lenz’s Law The induced B field in a loop of wire will oppose the change in magnetic flux through the loop. If you try to increase the flux through a loop, the induced field will oppose that increase! If you try to decrease the flux through a loop, the induced field will replace that decrease! Binduced Binduced

Flux and Change in Flux Magnetic flux is a vector that always points in the same direction as the magnetic field. However, it is really ΔΦ that we are interested in! If the flux is increasing, then ΔΦ points in the same direction as Φ. If the flux is decreasing, then ΔΦ points in the opposite direction as Φ.

Φ and ΔΦ Whiteboard State the direction of the flux and the change in flux through the loop in each of the following cases.

Φ and ΔΦ Φ: Into page ΔΦ: Into page Φ: Out of page ΔΦ: Out of page ΔΦ: Zero

Now On To Lenz’s Law! The induced current will flow so that its induced magnetic field opposes the change in flux. Iinduced Binduced

Lenz’s Law Challenge Lvl. I A loop of conducting wire is placed in the region shown below, in which the magnetic field is increasing in strength. Which way will the induced current flow in the loop?

Φ: Out of page ΔΦ: Out of page Binduced: Into page Iinduced: Clockwise

Lenz’s Law Challenge Lvl. II A loop of conducting wire is placed in the region shown below, and the loop is rotated 90° along the dotted line shown. Which way will the induced current flow in the loop while it is being rotated?

Φ: Out of page ΔΦ: Into page Binduced: Out of page Iinduced: Counterclockwise

Lenz’s Law Challenge Lvl. III The two wire loops shown below are moved at constant velocity near a current-carrying wire. Which direction, if any, will the induced current flow in each of the wire loops shown below? Loop 2 Loop 1 v v I

v v I Loop 2 Loop 1 Loop 1 Φ: Out of page ΔΦ: Zero Binduced: Zero Iinduced: None I Loop 2 Φ: Out of page ΔΦ: Out of page Binduced: Into page Iinduced: Clockwise

Faraday’s Law If there is an induced current in a loop of wire, it must be caused by an induced emf (voltage)! The induced emf has the same magnitude as the rate of change of the magnetic flux.

Getting Quantitative The loop of wire shown below has a radius of 0.2 m, and is in a magnetic field that is increasing at a rate of 0.5 T/s. The wire contains a 3 Ω resistor. r What is the induced emf? b) What is the induced current, and which way does it flow?

Since the area of the loop is constant, Solution Since the area of the loop is constant, Δ(BA) = AΔB ε = 0.06 Volts I = ε/R = 0.02 A clockwise

Quiz Tomorrow Lenz’s Law and Faraday’s Law Similar to HW problems and whiteboards Study it up!!