# Electromagnetic Induction

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Applets and Animations

Student Learning Objectives

• To observe the experimental evidence for electromagnetic induction.
• To understand the circumstances under which changing magnetic fields lead to induced currents.
• To understand how the movement of a conductor through a magnetic field leads to a motional emf.
• To understand and use Lenz’s law for induced currents.
• To use Lenz’s law and Faraday’s law to determine the direction and size of induced currents.
• To understand basic applications of electromagnetic induction to technology.

Lessons / Lecture Notes

PY106 Notes from Boston University (algebra-based):

HyperPhysics (calculus-based)

PHY2049 notes from Florida Atlantic University (calculus-based):

PHY2044 notes from Florida Atlantic University (calculus-based)

General Physics II notes from ETSU (calculus-based)

Important Equations

Example Problems

Problem 1
A 500-turn rectangular loop of wire has an area per turn of 4.5 × 10-3 m2. At t0 = 0 s, a magnetic field is turned on, and its magnitude increases to 0.50 T when t = 0.75 s. The field is directed at an angle of φ= 30.0o with respect to the normal of the loop. (a) Find the magnitude of the average emf induced in the loop. (b) If the loop is a closed circuit whose resistance is 6.0 Ω, determine the average induced current. (Solutions)

Problem 2
(a) A long, straight wire lies on a table and carries a current I. As shown in the drawing below, a small circular loop of wire is pushed across the top of the table from position 1 to position 2. Determine the direction of the induced current, clockwise or counterclockwise, as the loop moves past position 1 and position 2. Justify your answers. (Solutions)

(b) In the figure below, the magnetic field point out of the screen and is increasing in magnitude at a constant rate. Is the direction of the current through R to the right or left? (Solutions)

Applets and Animations
 Lenz's Law This interactive Java tutorial explores how the movement of a bar magnet influences induced current in a stationary conductor. Operating instructions appear below the tutorial window. Faraday's Electromagnetic Lab Play with a bar magnet and coils to learn about Faraday's law. Move a bar magnet near one or two coils to make a light bulb glow. View the magnetic field lines. A meter shows the direction and magnitude of the current. View the magnetic field lines or use a meter to show the direction and magnitude of the current. You can also play with electromagnets, generators and transformers! Motional EMF This applet shows the motional EMF generated by a rod moving in a constant magnetic field. The user can control the speed of the rod and the strength of the magnetic field. Falling Loop The Falling Loop Model shows a conducting loop falling out of a region of uniform magnetic field. It plots the velocity of the loop as a function of time. Users can change the size and orientation of the loop as well as the extent and location of the uniform field. How a Metal Detector Works This applets shows how a metal detector works. Metal detectors contain one or more inductor coils that are used to interact with metallic elements on the ground. The single-coil detector illustrated below is a simplified version of one used in a real metal detector. DC Electric Motor This Java applet shows a direct current electrical motor which is reduced to the most important parts for clarity. Instead of an armature with many windings and iron nucleus there is only a single rectangular conductor loop; the axis the loop rotates on is omitted. Generator This Java applet simulates a generator which is reduced to the most important parts for clarity. Instead of an armature with many windings and iron nucleus there is only a single rectangular conductor loop; the axis the loop rotates on is omitted. Electric Generator The Electric Generator Model shows a simple electric generator made from a conducting loop rotating in a uniform magnetic field and connected to an ammeter. The model shows a plot of the magnetic flux and induced current. Generator Generate electricity with a bar magnet! Discover the physics behind the phenomena by exploring magnets and how you can use them to make a bulb light.