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{Avg} = P{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{eff} = \frac{I{max}}{\sqrt{2}}
• V{eff} = \frac{V{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.