Phy 213 General Physics III Chapter 30 Induction

Phy 213: General Physics III Chapter 30: Induction & Inductance Lecture Notes

Electromagnetic Induction • We have observed that force is exerted on a charge by either and E field or a B field (when charge is moving): • Consequences of the Lorentz Force: – A B field can exert a force on an electric current (moving charge) – A changing B-field (such as a moving magnet) will exert a magnetic force on a static charge, producing an electric current → this is called electromagnetic induction • Faraday’s contribution to this observation: – 1. 2. 3. • • For a closed loop, a current is induced when: The B-field through the loop changes The area (A) of the loop changes The orientation of B and A changes A current is induced ONLY when any or all of the above are changing The magnitude of the induced current depends on the rate of change of 1 -3 q q N N S S Moving charge Moving magnet

Magnetic Flux • Faraday referred to changes in B field, area and orientation as changes in magnetic flux inside the closed loop • The formal definition of magnetic flux (FB) (analogous to electric flux): f When B is uniform over A, this becomes: • Magnetic flux is a measure of the # of B field lines within a closed area (or in this case a loop or coil of wire) • Changes in B, A and/or f change the magnetic flux Faraday’s Law: changing magnetic flux induces electromotive force (& thus current) in a closed wire loop

Faraday’s Law • When no voltage source is present, current will flow around a closed loop or coil when an electric field is present parallel to the current flow. • Charge flows due to the presence of electromotive force, or emf (e) on charge carriers in the coil. The emf is given by: i • An E-field is induced along a coil when the magnetic flux changes, producing an emf (e). The induced emf is related to: – The number of loops (N) in the coil – The rate at which the magnetic flux is changing inside the loop(s), or Note: magnetic flux changes when either the magnetic field (B), the area (A) or the orientation (cos f) of the loop changes:

Changing Magnetic Field A magnet moves toward a loop of wire (N=10 & A is 0. 02 m 2). During the movement, B changes from is 0. 0 T to 1. 5 T in 3 s (Rloop is 2 W). 1) What is the induced e in the loop? 2) What is the induced current in the loop?

Changing Area A loop of wire (N=10) contracts from 0. 03 m 2 to 0. 01 m 2 in 0. 5 s, where B is 0. 5 T and f is 0 o (Rloop is 1 W). 1) What is the induced e in the loop? 2) What is the induced current in the loop?

Changing Orientation A loop of wire (N=10) rotates from 0 o to 90 o in 1. 5 s, B is 0. 5 T and A is 0. 02 m 2 (Rloop is 2 W). 1) What is the average angular frequency, w? 2) What is the induced e in the loop? 3) What is the induced current in the loop?

Lenz’s Law • When the magnetic flux changes within a loop of wire, the induced current resists the changing flux • The direction of the induced current always produces a magnetic field that resists the change in magnetic flux (blue arrows) Magnetic flux, FB i i Increasing FB • Review the previous examples and determine the direction of the current

Operating a light bulb with motional EMF Consider a rectangular loop placed within a magnetic field, with a moveable rail (Rloop= 2 W). B = 0. 5 T v = 10 m/s L = 1. 0 m Questions: 1) What is the area of the loop? 2) How does the area vary with v? 3) What is the induced e in the loop? 4) What is the induced current in the loop? 5) What is the direction of the current?

Force & Magnetic Induction What about the force applied by the hand to keep the rail moving? • The moving rail induces an electric current and also produces power to drive the current: P = e. i = (5 V)(2. 5 A) = 12. 5 W • The power (rate of work performed) comes from the effort of the hand to push the rail – Since v is constant, the magnetic field exerts a resistive force on the rail: The force of the hand can be determined from the power:

Generators & Alternating Current • Generators are devices that utilize electromagnetic induction to produce electricity • Generators convert mechanical energy into electrical energy – Mechanical energy is utilized to either: • Rotate a magnet inside a wire coil • Rotate a wire coil inside a magnetic field – In both cases, the magnetic flux inside the coil changes producing an induced voltage – As the magnet or coil rotates, it produces an alternating current (AC) {due to the changing orientation of the coil and the magnetic field} • Motors and Generators are equivalent devices – A generator is a motor running in reverse:

Maxwell’s Equations Taken in combination, the electromagnetic equations are referred to as Maxwell’s Equations: 1. Gauss’ Law (E) 2. Gauss’ Law (B) 3. Ampere’s Law 4. Faraday’s Law

Significance of Maxwell’s Equations 1. A time changing E field induces a B field. 2. A time changing B field induces an E field. 3. Together, 1 & 2 explain all electromagnetic behavior (in a classical sense) AND suggest that both E & B propagate as traveling waves, directed perpendicular to each other AND the propagation of the waves, where: and The product, moeo, has special significance: or