Induction

Consider a conductor moving in a magnetic field…. X X X X X

The conductor is filled with mobile charges (by definition). X X X X X This causes, (induces) a current to flow. Each charge is a moving charge in a magnetic field, and will therefore have a force exerted on it. (RHR#3)

The conductor is filled with mobile charges (by definition). X X X X X We call this phenomena Electromagnetic Induction

In 1831 Michael Faraday in England, and Joseph Henry in the United States independently discovered electromagnetic induction…the production of electricity from magnetism. Faraday Henry

Who was the guy who did it the other way around? Discovered magnetism from electricity?

An electromotive force (emf) is produced in a conductor whenever it cuts across magnetic field lines. No emf arises from motion parallel to a magnetic field. Coil moves Down Coil moves Up Magnetic Field Lines

Calculating EMF EMF = Electromotive Force (Volts) B = Magnetic Field (T) L = Length of the wire (m) v = velocity of wire that is moving in the field (m/s)  = angle between wire and magnetic field

Lenz’s Law: The direction of an induced current is always such that its own magnetic field opposes the magnetic field responsible for producing it. Lenz’s law is a statement of the Law of Conservation of Energy

Drop a magnet through a conducting ring. N S A current will be induced in the ring. Consider a charge Q in the ring

Drop a magnetic through a conducting ring. N S The secondary magnetic lines of force always oppose the creating lines of force.

N S pull As the loop is pulled out of the field, a current will be induced in the loop.

N S pull Consider the force on this leg of the loop Induced force opposes original force

Usually it isn’t a single straight wire that is moving in a external magnetic field. Usually it is a coil of wires (like what you saw with the motor) that are rotating in the magnetic field. Alternating Current (AC)

B B B B B B Maximum EMF No EMF Maximum EMF

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Remember, a coil is just a solenoid with one loop & a solenoid creates a magnetic field just like a magnet

B B B B B DRAWTHISDRAWTHIS

Alternating Current (AC) This is how the electric company generates the electricity we use. Mechanical energy (spinning the coil) turns into electrical energy (EMF) The catch is figuring out what will spin the coil in the external magnetic field.

Effective Current & Effective Voltage Units: Amps I eff = effective current (average current) I max = maximum current Units: Volts V eff = effective voltage (average voltage) V max = maximum voltage In the USA, V eff = 120 V

Example: A generator is created by moving a 0.20 m long wire in an external magnetic field of 2.0 T at a speed of 15 m/s. (A) What EMF is produced by the generator? EMF = (2.0 T)(0.20 m)(15 m/s)sin90 o EMF = 6.0 V

(B) If the 6.0V is the maximum voltage produced by the generator, what is the effective emf? Veff = (6.0 V) Veff = 4.2 V

(C) If the generator is hooked up to a light bulb with a resistance of 2.5 , what is the effective power of the the bulb? Remember: P = IV = I 2 R = V 2 /R P eff = (V eff ) 2 /R P eff = (4.2) 2 /2.5 P eff = 7.1 W

Mutual Inductance Mutual inductance is a measure of the ability of one circuit carrying a changing current to induce an emf in a nearby circuit. The coil carrying the current initially is called the primary coil. The coil in which the current is induced is called the secondary coil.

Transformers Transformers are devices that change one AC potential difference to a different AC potential difference. Real transformers are not perfectly efficient. –Efficiencies of real transformers typically range from 90% to 99%. For this class, we will assume 100% efficiency. (We like living in an ideal world) :)

Residential Power Poles usually have 3 levels of wires. High Voltage 120 –240 Volts Telephone-Cable TV Transformer

There are two types of transformers: 1. Step up and 2. Step down

Step up vs Step down: Think of a staircase Step up: Start with a low voltage, end with a higher voltage Step down: Start with a high voltage, end with a lower one. VpVp VpVp VsVs VsVs

Transformers Volts x amps = Volts x amps in out

Transformer Equation WhereV = potential difference (voltage) N = # of turns in coil Subscript p refers to primary coil Subscript s refers to secondary coil

Example: A step up transformer is used on a 120 V line to provide a potential difference of 2400 V. If the primary has 75 turns, how many turns must the secondary have? V p = 120 V V s = 2400 V N p = 75 turns N s = ? N s = 1500 turns

Power for a transformer The power into a transformer equal the power out of a transformer