Electromagnetic Induction

What do we know? Hans Christian Oersted showed that moving

charges create a magnetic field.

Forces in Magnetism The existence of magnetic fields is known

because of their affects on moving charges. What is magnetic force (FB)? How does it differ from electric force (FE)? What is known about the forces acting on

charged bodies in motion through a magnetic field?• Magnitude of the force is proportional to the

component of the charge’s velocity that is perpendicular to the magnetic field.

• Direction of the force is perpendicular to the component of the charge’s velocity perpendicular to the magnetic field(B).

Magnetic Force (Lorentz Force)

FB = |q|vB sinθ Because the magnetic force is always

perpendicular to the component of the charge’s velocity perpendicular to the magnetic field, it cannot change its speed.

Force is maximum when the charge is moving perpendicular to the magnetic field ( = 90).

The force is zero if the charge’s velocity is in the same direction as the magnetic field ( = 0).

Also, if the speed is not changing, KE will be constant as well.

What is the magnetic field (B)? The magnetic field is a force field just like electric and

gravitational fields. It is a vector quantity. Hence, it has both magnitude and direction.

Magnetic fields are similar to electric fields in that the field intensity is directly proportional to the force and inversely related to the charge.

E = FE/q

B = FB/(|q|v)

Units for B: N•s/C•m = 1 Tesla

Two protons are launched into a magnetic field with the same speed as shown. What is the difference in magnitude of the magnetic force on each particle?

a. F1 < F2 b. F1 = F2 c. F1 > F2

Example 2: Lorentz Force

x x x x

x x x x

x x x x

v2

+

+ v1

F = qv x B = qvBsinθSince the angle between B and the particles is 90o in both cases, F1 = F2.

How does the kinetic energy change once the particle is in the B field?

a. Increase b. Decrease c. Stays the Same

Since the magnetic force is always perpendicular to the velocity, it cannot do any work and change its KE.

Faraday’s Hypothesis

If moving charges produced a magnetic field, could a moving or changing magnetic field produce a current?

Key Ideas Lorentz Force: A charge moving perpendicular to

a magnetic field will experience a force. Charged particles moving perpendicular to a

magnetic field will travel in a circular orbit. The magnetic force does not change the kinetic

energy of a moving charged particle – only direction.

The magnetic field (B) is a vector quantity with the unit of Tesla

Use right hand rules to determine the relationship between the magnetic field, the velocity of a positively charged particle and the resulting force it experiences.

Faraday’s Discovery

Faraday discovered that he could induce current by moving a wire loop through a magnetic field or moving the magnetic field through a wire loop.

Faraday’s Discovery is known as Electromagnetic Induction

Faraday's Discovery

Electromotive Force Last week we learned the Lorentz Force.

FB = qvB sinθ = BIL sinθ

When a conductor moves through a magnetic field, a force is exerted on these charges causing them to separate, inducing an EMF. Which end of the wire is positive?

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

v

L

Electromotive Force Last week we learned the Lorentz Force.

FB = qvB sinθ = BIL sinθ

When a conductor moves through a magnetic field, a force is exerted on these charges causing them to separate, inducing an EMF.

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

v

+

-

L

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

I

vF

I

-

+

Electromotive Force The EMF results when the conductor has a velocity

component perpendicular to the magnetic field.

Use RHR #1 where the thumb points in the direction of the velocity. The force on the bar is opposite the velocity.

I

Example 1: EM Induction

A segment of a wire loop is moving downward through the poles of a magnet, as shown. What is the direction of the induced current?

a. The current direction is out-of the page to the left.b. There is no induced current.c. The current direction is into the page to the right.

Example 2: EM Induction The drawing shows three identical rods (A, B, and C)

moving in different planes in a constant magnetic field directed along the +y axis. The length of each rod and the speeds are the same, vA = vB = vC. Which end (1 or 2) of each rod is positive?

Rod A:

a. 1 b. 2 c. neither

Rod B:

a. 1 b. 2 c. neither

Rod C:

a. 1 b. 2 c. neither

Magnetic Flux

What is magnetic flux? Like electric flux A measure of the strength of the magnetic field, B,

passing through a surface perpendicular to the field. For a bar magnet, the flux is maximum at the poles. The more magnetic field lines, the higher the flux.

=BAcos

x x x x x xx x x x x xx x x x x xx x x x x x

Iv

F

I

-

+

Magnetic Flux and EMF We already know:

EMF = vBL

v = Δx/Δt = (x – xo)

(t – to)

EMF = (Δx/Δt)BL = (xL – xoL) B = (BA) – (BAo)

(t – to) (t – to)

EMF = -ΔΦ/Δt Where:

= BA cos and = the angle the normalto the surface makeswith B (in this drawing itis 0o).

Faraday’s Law of EM Induction In the drawing on the previous slide, there is

only one loop in the circuit. When there is more than one loop in a circuit, as

in the coil of a solenoid, the EMF induced by a changing magnetic field will increase by a factor equal to the number of loops in the coil.

EMF = -N ΔΦ/Δt

Where N = the number of loops in the coil.

Lenz’s Law Per 6 & 7 The induced EMF resulting from a changing

magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change.

If the magnetic field is increasing, a current will develop to oppose the increasing magnetic field.

If the magnetic field is decreasing, a current will develop to create a magnetic field in the same direction as the one that is decreasing.

A current will form that attempts to keep the magnetic field constant.

Lenz’s Law abides by the laws of conservation of energy.

Lenz’s Law

Lenz's Law

Lenz’s Law

Current will be induced in the copper ring when it passes through a region where the magnetic field changes. When the magnetic field is constant or absent, their will be no induced current.

x x x x x x

x x x x x x

x x x x x x

x x x x x x

No Current

No Current

No Current

InducedCurrent

InducedCurrent

Applications of Lenz’s Law (Eddy Currents) Eddy current balances. Eddy current dynamometer. Metal detectors (Lenz's Law) Braking systems on trains. What are Eddy currents?

Eddy currents are currents created in conductors to oppose the changing magnetic fields they are exposed to.

Eddy currents respond to the changes in an external magnetic field.

Eddy currents can form in conductors even if they are not capable of being magnetized.