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 LawThe 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!

BinducedBinduced

Flux and Change in Flux

Magnetic flux is a vector that always points in the same direction as the magnetic field.

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.

However, it is really ΔΦ that we are interested in!

Φ and ΔΦ WhiteboardState the direction of the flux and the change in flux through

the loop in each of the following cases.

Φ and ΔΦ

Φ: Into pageΔΦ: Into page

Φ: Out of pageΔΦ: Out of page

Φ: Out of pageΔΦ: Into page

Φ: Out of pageΔΦ: Zero

Now On To Lenz’s Law!

The induced current will flow so that its induced magnetic field opposes

the change in flux.

Binduced

Iinduced

Lenz’s Law Challenge Lvl. IA 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. IIA 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. IIIThe 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?

v

I

vLoop 1

Loop 2

v

I

Loop 2

vLoop 1

Loop 1

Φ: Out of page

ΔΦ: Zero

Binduced: Zero

Iinduced: None

Loop 2

Φ: Out of page

ΔΦ: Out of page

Binduced: Into page

Iinduced: Clockwise

Faraday’s LawIf 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

r

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.

a) What is the induced emf?b) What is the induced current, and which way does it flow?

SolutionSince the area of the loop is constant,

Δ(BA) = AΔB

a) ε = 0.06 Voltsb) 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!!