Electromagnetic Electromagnetic InductionInduction

The Discoveries of Michael The Discoveries of Michael Faraday and Joseph Henry Faraday and Joseph Henry Showed That a Current Can Showed That a Current Can Be Induced by a Changing Be Induced by a Changing Magnetic Field.Magnetic Field.

Faraday’s LawFaraday’s Law• An emf is set up in a closed An emf is set up in a closed

electric circuit located in a electric circuit located in a magnetic field whenever the magnetic field whenever the total magnetic flux linking the total magnetic flux linking the circuit is changing.circuit is changing.

• This is called This is called electromagnetic electromagnetic inductioninduction..

• Induced emf• Induced current

A Galvanometer and A Galvanometer and a B-Fielda B-Field

• Induced current is related to the Induced current is related to the motion of the conductor in the motion of the conductor in the magnetic fieldmagnetic field

• The direction of the induced current is The direction of the induced current is directly related to the direction of directly related to the direction of motion of the conductor in the motion of the conductor in the magnetic fieldmagnetic field

• Direction is dependent on the motion Direction is dependent on the motion of the B-field or the conductorof the B-field or the conductor

• The motion of the conductor is The motion of the conductor is perpendicular to the B-fieldperpendicular to the B-field

More Thoughts…More Thoughts…• If the conductor is moved parallel to If the conductor is moved parallel to

B-field, the galvanometer will show B-field, the galvanometer will show no deflection, thus no induced emf or no deflection, thus no induced emf or current.current.

• If the conductor is looped several If the conductor is looped several times, the deflection on the times, the deflection on the galvanometer will increase.galvanometer will increase.

• Thus, the rate of motion, the number Thus, the rate of motion, the number of loops and the magnitude of the B-of loops and the magnitude of the B-field vary directly with the magnitude field vary directly with the magnitude of the induced current and emf.of the induced current and emf.

Factors Affecting EmfFactors Affecting Emf

• Emf induced in each coil of the Emf induced in each coil of the conductor is proportional to rate conductor is proportional to rate of change of magnetic fluxof change of magnetic flux

• Emf = - Emf = - tt• Emf = -N(Emf = -N(t)t)

• Note that negative sign Note that negative sign indicates that induced emf is of indicates that induced emf is of such polarity as to oppose the such polarity as to oppose the change that induced itchange that induced it

Induced EMFInduced EMF

• Induced current exists only if Induced current exists only if wire in a field is part of a wire in a field is part of a circuit.circuit.• Thus, if Thus, if = BA then = BA then = Bxl = Bxl• So therefore, Emf = So therefore, Emf = Bxl/Bxl/tt

• But x/t = v (velocity)But x/t = v (velocity)• Therefore, Emf = BlvTherefore, Emf = Blv

Faraday’s LawFaraday’s Law

The induced emf in a coil The induced emf in a coil of N loops with a of N loops with a changing B – field within changing B – field within in equal to the rate of in equal to the rate of change of magnetic flux change of magnetic flux times the number of times the number of loops.loops.

tNEmf

Lenz’s LawLenz’s Law

The net B-field thru a loop The net B-field thru a loop from a changing flux from a changing flux comes from two sources.comes from two sources.

•The original B – field.The original B – field.•The B – field caused by The B – field caused by the original current…the original current…the induced B – field.the induced B – field.

Induced B – FieldInduced B – Field

This occurs because of This occurs because of the induced current.the induced current.

This can be used to This can be used to determine the polarity determine the polarity of the induced emf.of the induced emf.

Lenz’s LawLenz’s Law

The induced emf resulting from a The induced emf resulting from a changing magnetic flux has a changing magnetic flux has a polarity that leads to an polarity that leads to an induced current whose induced current whose direction is such that the direction is such that the induced B – field opposes the induced B – field opposes the original flux change.original flux change.