Electromagnetic Induction Notes

Electromagnetic Induction

11.1 Inducing Currents

• Learning Objectives:

  • Identify how a changing magnetic field produces an electric current.
  • Define electromotive force.

• Key Vocabulary:

  • Electric generator
  • Electromagnetic induction
  • Induced electromotive force

Changing Magnetic Fields

• An electric current can be generated in a wire in a circuit when at least part of the wire moves through, and cuts, magnetic field lines.
• Field lines can be cut when:
  1. A segment of wire moves through a stationary magnetic field.
  2. A magnetic field moves past a stationary wire.
  3. The strength of a magnetic field changes around a wire.
• It is the relative motion between a wire and a magnetic field that can produce current.
• Electromagnetic induction is the process of generating current through a wire in a circuit in a changing magnetic field.

Electromotive Force (EMF)

• The potential difference given to the charges by a battery or a generator is called the electromotive force (EMF).
• Electromotive force is not actually a force; instead, it is a potential difference and is measured in volts.
• When you move a wire through a magnetic field, you exert a force on the charges, and they move in the direction of the force. Work is done on the charges.
• Their electrical potential energy, and thus their potential, is increased.
• This difference in potential is called the induced electromotive force (induced EMF).

Factors Affecting Induced EMF

• The EMF of a wire moving in a magnetic field depends on:
  1. Magnetic field (B)
  2. The length of the wire in the magnetic field (L)
  3. Velocity of the wire in the field that is perpendicular to the field $(v \sin \theta)$
• $\theta$: is the angle between B and v.
• Remember Ohm's Law: $\text{EMF} = BLv \sin \theta$

Direction of Current

• To find the force on the charges in the wire, use the fourth right-hand rule:
  • Hold your right hand so that your thumb points in the direction in which the wire is moving, and your fingers point in the direction of the magnetic field.
  • The palm of your hand will point in the direction of the conventional (positive) current.

Induced EMF in a Wire

• Ohm's Law: $I = \frac{\Delta V}{R}$

Example 1: Induced EMF

A straight wire is part of a circuit that has a resistance (R) of 0.50 $\Omega$. The wire is 0.20 m long and moves at a constant speed of 7.0 m/s perpendicular to a magnetic field of strength $8.0 \times 10^{-2}$ T.

• a. What EMF is induced in the wire?
  • $EMF = BLv(\sin \theta)$
• b. What is the current through the wire?
  • $I = \frac{EMF}{R}$
• c. If a different metal were used for the wire, increasing the circuit's resistance to 0.78 $\Omega$, what would the new current be?
  • $I = \frac{EMF}{R}$

Induced EMF in Microphones

• A microphone is a simple application that depends on an induced EMF to convert sound waves to electrical signals.
• The microphone has a diaphragm attached to a coil of wire that is free to move in a magnetic field.
• Sound waves vibrate the diaphragm, which moves the coil in the magnetic field, inducing an EMF across the ends of the coil.
• The induced EMF varies as the frequency of the sound varies.
• In this way, the sound wave is converted to an electrical signal.

Electric Generators

• An electric generator converts mechanical energy to electrical energy.
• An electric generator consists of a number of wire loops placed in a strong magnetic field. The wire may be wound around an iron core to increase the strength of the magnetic field (armature).
• The armature is mounted so that it can rotate freely in the magnetic field.
• As the armature turns, the wire loops cut through the magnetic field lines and induce an EMF.
• When a generator is connected in a closed circuit, the induced EMF produces an electric current.
• The EMF developed by the generator depends on the length of the wire rotating in the field.
• Increasing the number of loops in the armature increases the wire length, which increases the induced EMF.
• The direction of the induced current can be found from the third right-hand rule.
• As the loop rotates, the strength and the direction of the current change.
• The current is greatest when the loop’s velocity is perpendicular to the magnetic field.
• As the loop rotates, it moves through the magnetic field lines at an ever-increasing angle. Thus, it cuts through fewer magnetic field lines per unit of time, and the current decreases.
• When the loop is in the vertical position, the wire segments move parallel to the field, and the current is zero.
• As the loop continues to turn, the segment that was moving up begins to move down and reverses the direction of the current in the loop.
• This change in direction occurs each time the loop turns through 180°.
• The current changes smoothly from zero to some maximum value and back to zero during each half-turn of the loop.
• Then it reverses direction.
• Generators and motors are almost identical in construction, but they convert energy in opposite directions.
• A generator converts mechanical energy to electrical energy, while a motor converts electrical energy to mechanical energy.

Power in AC Circuits

• The power produced by a generator is the product of the current and the voltage.
• Because both current and voltage vary, the power associated with an alternating current varies.
• Note that power is always positive because I and V are either both positive or both negative.
• Average power, PAC, is half the maximum power:
  • $P<em>{Avg} = P</em>{AC} = \frac{P_{max}}{2}$

Effective Current and Voltage

• It is common to describe alternating current and voltage in terms of effective current and voltage rather than referring to their maximum values.
• $I<em>{eff} = \frac{I</em>{max}}{\sqrt{2}}$
• $V<em>{eff} = \frac{V</em>{max}}{\sqrt{2}}$
• Effective voltage is also commonly referred to as RMS (root mean square) voltage.
• In the United States, $V_{eff} = 120$ V for most wall outlets. The actual voltage oscillates at a rate of 60 Hz.
• The frequency and effective voltage that are used vary in different countries.