Chapter 20Magnetic FluxFaraday’s Law

We saw in Chapter 19 that moving charges (currents) create magnetic fields. Nature often reveals a great deal of symmetry. So, scientists wondered, “Can magnetic fields can create currents?” You might guess that the answer is, “Yes.” In this chapter, we’ll explore this physical process known as induction.

Induced Voltages and Inductance

Shortly after Oersted’s discovery that currentscreate magnetic fields, Michael Faraday (England)and Joseph Henry (US) conducted experimentsto determine if magnetic fields created electricalcurrents...

Primary Circuit

primary coil secondary coil

Secondary Circuit

+ _A

Soft magneticmaterial

+ _A

Faraday’s Observations:

With the switch open, no reading on the ammeter.

When the switch is closed, the ammeter needle deflects momentarily toward the right, then returns to 0.

+ _A

Faraday’s Observations:

When the switch is opened, the ammeter needledeflects to the left momentarily, then returns to 0.

With a constant current flowing through theprimary circuit, the ammeter shows no reading.

+ _A

Faraday’s Conclusions:

Steady currents in the primary produce constant magnetic fields, which result in no current in the secondary circuit.

Changing currents in the primary circuit result in changing magnetic fields, which result in induced currents in the secondary circuit.

A

SN

If we move a bar magnet toward a loop ofwire, the ammeter deflects to the left.

When we stop moving the magnet, theammeter reads 0.

When we pull the magnet away from the loop,the ammeter deflects to the right.

As the magnet moves toward the loop, themagnetic field near the loop increases.

As the magnet moves away from the loop, themagnetic field near the loop decreases.

Such results are consistent with Faraday’sexperiment: Changing magnetic fields leadto induced currents.

A

SN

x x x x x

x x x x x

x x x x x

x x x x x

side view

MagneticFlux

One way to think about this is to simply count the number of magnetic field lines passing through a loop.

How much magneticfield is passing throughthe loop?

x x x x x

x x x x x

x x x x x

x x x x x

side view

30o

60o

top view

Magnetic flux is the amount of magnetic fieldperpendicular to the loop.

If you separate the magnetic field intocomponents parallel and perpendicularto the loop, you see that...

30o

60o

top view =| |A =| |AB B cos

Btot

B B||

This is also the direction of the normal to the loop!

= B A = BA cos

= B A cos

T mWb

mm Wb2

22

So, the Weber is the unit of magnetic flux.

What is the magnetic flux through a square loop of side length 10 cm whose normal is at an angle of 60o to the direction of a uniform magnetic field of strength 1 T?

= B A = BA cos

= ( )(. ) cos1 1 602T m o

= 5 10 3 Wb

Having defined the magnetic flux, we cannow quantify the induced EMF we haveseen in the secondary circuit.

Nt

EMF! N is the number of turns

What causes currents to flow? PotentialDifferences