11.1 Electromagnetic induction

Rectangular coil with N turns

- A current only flows when one side of the coil is moving through the magnetic field and the other side is outside the field. - if the whole coil was inside the magnetic field, each side would generate an emf - the two emfs would oppose one another and no current would flow

Derived formula for induced emf

- ε=Blv - v= ∆x/∆t - ε= Bl∆x/∆t - but Bl∆x=∆A - ε=B∆A/∆t

right hand rule

-Assume that you are holding a wire -If your thumb points in the direction of the positive current of the wire, your fingers encircling the wire show the magnetic field's direction -The thumb, therefore, points to the north pole

One change to increase the maximum induced emf

1. Decrease the RESISTANCE 2. Decrease the CAPACITANCE

What does an induced emf depend on?

1. speed of the wire 2. the strength of the magnetic field 3. The length of the wire

The current registered by the galvanometer is increased when?

1. the relative speed of the magnet increases 2. the strength of the magnet increases 3. the number of turns increases 4. the area of the loop increases 5. the magnet moves at right angles to the plane of the loop

Explain how the magnetic forces acting between the cables vary during the course of one cycle of the alternating current (ac)

1. wires attract when the current is in the SAME direction 2. charge flow in both wires is always the same but reverse every half-cycle (180°) 3. Force is max twice in a cycle (at 90° and 270°)

Magnetic flux

A measure of the amount of field lines passing through an area, at right angles to that area can be increased by increasing the area or the concentration of fieldlines and is maximum when field lines are at right angles to area. - BAcosθ - unit= weber = 1Wb= 1Tm² - the number of field linesthat cross or pierce the loop area. - What counts is the part of the loop area that is pierced by magnetic field lines.

An emf is induced across the wings of an aircraft as it takes off and continues on its flight-path. Give two reasons why the induced emf may be greater during the aircraft's flight-path than during take-off.

Aircraft is moving faster so rate of flux cutting is greater, angle at which flux is cut may be close to 90°

induced emf

Amount of mechanical energy converted into electrical energy per unit charge. 1. When a conductor moves through a magnetic field the "free electrons" also move (right to left). 2. The magnetic field will exert a force on these moving electrons. In this case the force is downwards which means the electrons will be pushed downwards. 3. This creates at the bottom end of the conductor a net negative charge and on the top an equal net positive charge. 4. The flow of electrons towards the bottom will stop when the electrons already there are numerous enough to push any new electrons back by electrostatic repulsion. WHENEVER LINES OF MAGNETIC FLUX ARE CUT

Coil rotating

At some stage, the conducting rod will reach the end of the contacts, or the coil will move past the magnetic field. With a rotating coil, we can induce an emf without having these constraints. - every 180° the coil's direction reverses

Uniform field

B= ∅/A

Electric field in an induced emf

E= emf/ L - emf= potential difference between the ends of the rod (induced emf) - The flow of electro s will stop when the electric force eE pushing the electrons back equals the magnetic force evB: eE= evB

Flux linkage

It is just magnetic flux but multiplied by number of turns in a coil. Rate of change of linkage determines induced emf. The total number of times any field line crosses any single one of these areas NBAcosθ flux linkage= N∅

When does the maximum flux occur?

It occurs when the angle is 90

Changing magnetic flux linkage

Magnetic field can create an electric current - As a magnetic brought closer to the loop area, the magnetic field at the loop and the flux is increasing. -If the magnet is held stationary near the loop, the flux through the loop is not changing, nothing happens. - if the number of turns is increases, so is the flux linkage.

Important info for Φ =BAcosθ

Remember, θ in this equation is the angle the field makes to the normal of the plane of the loop. Often, in an exam, the angle between the field and the plane of the loop is provided to you. In these situations you must use 90−θ as the angle, or use sin instead of cos

Lenz's Law

The direction of the induced emf is such that if an induced current were able to flow, it would oppose the change which caused it. - conservation of energy = the electrical energy generated within any system must result from work being done on the system - When a conductor I moved through a magnetic field and an induced current flows, an external force is needed to keep the conductor moving. This provides energy for the current to flow. - If the direction of an induced current did not oppose the change that caused it. Then it would be supporting the change. - A force would be generated that further accelerated the mocing object which would generate an even greater emf- electrical energy done without any work done.

Faraday's Law

The induced emf is equal to the negative rate of change of magnetic flux linkage ε= - N∆∅/∆t So the emf is induced. If the emf is induced in a conductor then there will be a current as well. - The "-" does not concern us but we need it in calculus. - The magnitude of an induced emf is proportional to the rate of change of flux linkage.

What happens when the angle is 90?

The magnetic flux will be 0 , the value will then be BA

emf

The potential difference measured when two half-cells are connected resulting from a source of electrical power. example: internal voltage or potential difference

Using Faraday's law

The rod cuts magnetic field lines as it moves in the magnetic field. In time ∆t it will move a distance of v∆t and so the flux through the area swept by the rod is: ∆∅=BLv∆t ε= ∆∅/∆t ε=BvL

Rod on two wires joined by a resistor of R

There is a potential difference between the top and the bottom equal to BvL and a current equal to I= BvL/R. - This is because electrons in the bottom part of the circuit now have the opportunity move up through the resistor, thus momentarily reducing the number of electrons in the bottom. - The electric field in the rod is reduced and so the downward magnetic force on the electrons pushes more electrons down. - since there is current the rod needs to be pushed if it is to continue to move at constant speed. This is because the rod carries a current and is in a magnetic field, so it experiences a magnetic force F directed to the left: F=BIL = B (BvL/ R)L = vB²L²/R

Left hand rule

Thumb= Motion= Current=

Magnetic flux density

a measure of the strength of the magnetic field defined in terms of the force on a current-carrying conductor at right angles to the field lines. Field Strength is defined as the force per unit current legth on a wire placed perpendicularly to the magnetic field.

motional emf

conductor of length (l) moving with velocity (v) perpendicular to a magnetic field (B) will have a potential difference BvL across its ends.

What is the size of the induced emf dependent on?

the rate at which field lines are cut

unit of magnetic flux

unit= weber = 1Wb= 1Tm²

Faraday and Lenz's law

ε= - N∆∅/∆t