Physics - Electromagnetism

Electric Fields

F = Eq

• F – force acting on charged particles (N)

• E – electric field strength (Nc-1 )

• q – charge of an object experiencing the force (C)

Electric Field between Two Plates

E = v/d

A charge placed anywhere in a uniform field will experience a constant electric field (F=Eq). Therefore, acceleration is also constant (F=ma).

Work in Electric Field

WORK DONE CONVERTS TO ELECTRIC POTENTIAL AND KINETIC ENERGY

W = qV

• W – work (J)

• q – charge of an object experiencing the force (C)

• V – electrical potential (V or JC-1 )

W = qEd - UNIFORM ELECTRIC ONLY

• W – work (J)

• q – magnitude of charge (C)

• E – electric field strength (NC-1 )

• d – distance between points, parallel to the electric field (m)

Charged Particle in Magnetic Field

F = Bvqsin𝜃

• F – force (N)

• q – charge (C)

• v – velocity of charged particle (ms-1 )

• B – magnetic field strength (T)

• 𝜃 – angle the object is moving at with respect to the magnetic field

Right Hand Rule

Thumb points in the direction of the conventional current.

Fingers point to the direction of the magnetic field.

Palm faces the direction of force.

Effect of a Charged Particle in a Magnetic Field

• If a charge were to enter a magnetic field perpendicular, it will undergo circular motion & experience centripetal motion.

• Therefore, the magnetic force on the charge is equivalent to its centripetal force

F = mv² / r

r = mv / qB

Motor Effect

F = BIlsin𝜃

• When a current-carrying conductor is placed in a magnetic field, it experiences a force.

• A moving charge with a constant velocity produces a magnetic field.

• Electrons move as a stream in conductor with uniform velocity & produces a magnetic field surrounding the conductor.

• It converts EPE to KE.

• This magnetic field interacts with an external magnetic field, which causes a constant field in the same direction acting on the conductor.

Force between parallel current carrying conductors

F/L = 𝜇0 x I1 x I2 / 2 (pi) r

• Same attract

• Different Repel

Electromagnetic Induction

Michael Faraday discovered that an electric current can be induced in a conductor if there was a change in the magnetic field acting on that conductor.

• Faraday demonstrated that a change in magnetic field would result in an induced electromotive force (EMF) that in turn produces inducing current.

• This would be done by moving a magnet near a conductor & observe the needle of a galvanometer deflect in a certain direction.

  • A deflection in a galvanometer indicates a producing current.

Magnetic Flux

Flux = BAcosθ

A measure of the total magnetic field that passes through a particular area.

• Measured in Webes (Wb)

Faraday’s Law

“The induced EMF, in a closed circuit, is directly proportional to the rate of change of magnetic flux.”

ε = -N dΦ/dt

• ε – induced EMF (V)

• n – number of loops

• Δ𝜙 – change in magnetic flux (Wb)

• Δt – change in time (seconds)

Lenz Law

“An induced EMF always gives rise to a current whose magnetic field will oppose the original change in flux”

Lenz’s Law accounts for the negative sign in Faraday’s law. The current induced in the coil opposes any change in the magnetic flux by flowing opposite to the current which caused such changes.Thus, this law is used to explain the direction of the induced EMF

Eddy Current

• It is a special type of current that is induced when a metal plate experiences a change in magnetic flux.

• Lenz’s Law governs the direction of eddy currents’ flow in a loop

Transformers

• They allow generated AC voltage to either by increased or decreased before it is used.

• They function by mutual induction where a changing current in one coil causes an induced EMF in the area of another coil.

• A transformer has two coils (primary & secondary coils) of conducting wires wound on a laminated iron core.

• Iron core:

  • Material with high permeability to concentrate & guide the magnetic field lines inside the core.

• AC current is fed into the primary coil which induces a current in the secondary coil.

• AC current switches current direction periodically, which results in a changing magnetic field.

• The secondary coil experiences a change in magnetic flux; therefore, AC current is induced.

Vp / Vs = Np / Ns = Is / Ip

Types of Transformers

Step Up:

• Increase secondary voltage, therefore decreasing current in second coil.

Step Down:

• Decrease secondary voltage, therefore increasing current in second coil.

Power loss in Transmission Lines

• Eddy Currents: loops in core - laminated iron.

• Hysteresis Loss: repeated magnetism - use soft iron cores.

• Restrictive Heating: current in wires - thick, low resistance copper.

P loss = I² R

DC Motors

A DC motor is a device which converts electrical energy into mechanical energy. DC current is fed through a coil in a magnetic field, which produces a rotation motion due to the motor effect.

• Armature

• Coil

• Stator - Permanent/Electromagnets.

• Split Ring Commutator

• Brushes

• Power Supply

Torque in DC

T = nBIA x sinθ

Back EMF

• Back EMF is the induced EMF produced in the coil of a motor due to its rotation in a magnetic field.

• The rotation supplies the change in flux, thus a current is induced (Faraday’s Law).

• As a consequence of Lenz’s Law, the induced EMF opposes the change that causes it & therefore acts in the opposite direction to the EMF creating it.

• Therefore, back EMF works against the input voltage from the power supply.

• Back EMF reduces the net EMF

• ↑ loads = ↓ speed of rotation = ↓ back EMF = ↑ current

• ↑ loads (slower rotations) = ↑ currents in the coil.

• ↑ current = ↑ torque (sacrificing heat production).

• Back EMF keeps dropping until a high enough current & torque is reached to meet the load experiment.

• When the motor comes to a sudden halt (drill gets stuck), back EMF will be completely removed.

• This leads to extremely high currents that could burn out the motor.

• When a DC motor starts, there is little back EMF or rotation. This means the coil experiences the full initial current.

Generators

A generator is a device which converts mechanical energy into electrical energy by applying the principle of electromagnetic induction.

• A coil of wire is forced to rotate about an axis in a magnetic field.

• This causes the coil to experience a change in magnetic flux, inducing an EMF (Faraday’s Law). This then transferred to an external circuit.

AC: Slip Ring DC: Split Ring

AC Induction Motor

They use the principle of electromagnetic induction to rotate the rotor, instead of the motor effect in traditional motors.

• AC has a stator and rotor, just like DC.

• The rotor is an assembly of parallel conductors & end rings. They produce a similar shape to ‘squirrel cages’.

• The stator is the stationary electrical component, which is made up of pairs of electromagnets connected to an AC power supply.

• The coils are wound in a way that when a current flows through the coils, one coil would be the north pole & its pair a south pole.

• Initially, one pair of electromagnets is fed AC current to produce a magnetic field, while the remaining two pairs do not.

• Due to the nature of the AC power supply, this pair is then turned off & the adjacent pair is turned on.

• This process continues, ultimately producing rotating magnetic field

• Due to the rotating magnetic field, an electric current is induced in the rotor (Faraday’s Law). This induced electric current produces its own magnetic field.

• Due to Lenz’s Law, this magnetic field is induced in such a way that opposes the change that causes it, effectively causing the rotor to spin the same direction as the rotating magnetic field.

Cost Effective, Reduced maintenance (no wear)