6.3 electromagnetism

magnetic field

a region of space where moving charged particles are subject to a magnetic force
they can be created by permanent magnets or moving charges, and magnetic fields interacting result in a magnetic force

direction of a magnetic field

north pole to south pole

permanent magnet

a material that produces a magnetic field

magnetic field lines

aka lines of magnetic flux- lines showing the shape and direction of a magnetic field
equally spaces and parallel field lines demonstrate a uniform magnetic field, magnetic fields are rarely fully uniform athough they may have uniform segments

MFL wire

magnetic fields circle the wire

MFL flat coil

magnetic field goes through the center of the coil

MFL solenoid/barmagnet

magnetic fields loop from the North side to the South
if two are placed next to eachother, the fields can join in a circle if they are oppositely charged

wires in magnetic fields

a current-carrying wire placed into a magnetic field will eperience a force due to the interaction of its magnetic field and the external magnetic field

fleming's left hand rule

a way of remembering the directions of the force, current and magnetic field when a wire is placed into a magnetic field
a mnemonic to remember is FBI (force, magnetic field, current) which corresponds to the 3 fingers in order
(inc diagram)

fleming's LHR equation

F = BILsin𝜃
where F is force(N), B is magnetic field strength(T or Wb/m^2), I is current(A), L is the length of the wire(m) and 𝜃 is the angle between the direction of the current and the direction of the magnetic field (its sine is 1 at a right angle)

magnetic flux

the total magnetic field (flux) passing through a given area
Φ = BAcos𝜃, where Φ is magnetic flux (Wb), B is magnetic field strength, A is area, and 𝜃 is the angle between B and the normal to the surface

magnetic field strength

aka magnetic flux density- the amount of magnetic flux per unit area
denoted as B

techniques to determine magnetic flux density- method

-a horseshoe magnet is placed on a set of digital balance scales, and the scales are zeroed out
-a rigid straight wire is connected to a DC power supply and a variable resistor and an ammeter in series
-the wire is aligned with the bar magnet such the force on it will be upwards
-the length of the wire in the field is measured
-the wire is turned on, and the reading on the scaled is recorded for different values of current (altered by varying the resistance of the circuit)

techniques to determine magnetic flux density- results

a graph is plotted of the mass registered on the scale versus the current of the wire
the gradient of the graph is found
the magnetic force on the wire and the weight of the magnet are equalled to give mg = BIL
this equation is rearranged to m = BIL/g and thus ∆m/∆l = BL/g to conform it to the gradient equation y = mx + c
as g is known and L is measures, the magnetic flux density can be determined using the gradient

charged particles in uniform magnetic fields equation

the magnetic force on an isolated moving charged particle in a magnetic field is given by:
F = BQvsinθ
where F is force(N), B is m.f.d(T), Q is charge(C) and v is the speed of the particle(m/s) and θ is the angle between the direction of the magnetic field and the movement of the particle (1 when perpendicular, 0 when parallel)

charged particles in umf and circular motion

a charged particle in a uniform magnetic field moving perpendicular to the magnetic field will experience circular motion as the magnetic force provides centripetal force

centripetal force equation

F = mv^2
where F is the centripetal force(N), m is the mass of the particle(kg), v is the linear velocity of the particle(m/s) and r is the radius on the orbit(m)

centripetal force and charged particles in magnetic fields equation

Bqv = mv^2/r
as the centripetal force is the magnetic force

velocity selectors

devices consisting of perpendicular electric and magnetic fields where charged particles with a specific velocity can be filtered for

velocity selector equation

v = E/B
where v is the velocity being selected for (m/s), E is the electric field strength and B is the magnetic field strength

magnetic flux linkage

the magnetic flux multiplied by the number of turns in a coil
flux linkage = ΦN = BAN
unit is weber turns

faraday's law

the induced electromotive force in a coil is proportional to the rate of change of magnetic flux linkage
ε = Δ(Nɸ)/Δt
where ε is the induced emf (V), Δ(Nɸ) is the change in magnetic flux linkage(Wb turns) and Δt is the time

lenz's law

the direction of the induced electromagnetic force opposes the change in flux that caused it

electromagnetic induction

when a current is induced due to a change in the magnetic flux linkage, for example by moving a wire through a non-uniform magnetic field or varying the strength of the magnetic field

calculating induced emf

combining the lenz's and faraday's laws gives:
ε = -Δ(Nɸ)/Δt
(as lenz's law is used to negate the faraday law equation due to the opposing direction of the emf and the causing flux)

induced emf in a rotating coil

ε = BANωsinθ
where ε is the induced emf(V), B is the magnetic flux density(T), A is the cross-sectional area of the inside of the coil (m^2), N is the number of turns in the coil, ω is the angular velocity of the rotating coil(rad/s), and θ is the angle between the magnetic field and the normal to the cross-sectional area of the coil(rad) (maximum when 90, minimum/none at 0)

generators

a device that generates energy by rotating a rectangular coil of wire in a uniform magnetic field between two large oppositely charged magnets using an external force (e.x. coal power stations burn coal to evaporate water and use the vapor to turn the coil)

alternators and dynamos

alternators generate ac (alternating current) while dynamos generate dc (direct current)

transformers

devices that change low alternating voltages at high currents to high alternating voltage at low currents (step-up) and vice versa (step-down)
designed to reduce energy loss through heat while transmitting electricity along power lines as high currents release more heat energy than high voltages

transformer anatomy

a soft iron core (shaped like a rectangle with a rectangle-shaped hole through the middle) is wrapped with a coil of wire on either end, each with a different number of turns (primary and secondary coil)

transformer function

-an alternating current is applied to the primary coil which creates an alternating magnetic field, and thus a changing magnetic flux linkage, inside the iron core
-the iron core transfers the changing magnetic field onto the secondary coil, inducing an electromotive force and thus an alternating output voltage
-the difference in the number of coils causes a change in the voltage
-step-up transformers have more coils in the secondary coil and step-down transformers have more coils in the primary coil

transformer equation

for a completely efficient transformer:
Vp/Vs = Np/Ns = Is/Ip
where V is voltage, N is number of turns and I is current, and p and s respond to the primary and secondary coils respectively

efficiency of a transformer

e = IsVs/IpVp

investigating transformers

-wind 5 loops of copper wire (primary coil) on one end of an iron bar and 10 loops around the other (secondary coil)
-connect a multimeter across each coil and connect the primary coil to a low voltage ac supply
-turn off the AC supply then record the current and voltage across each coil
-repeat for different combinations of loop numbers
-find Vp/Vs, Np/Ns and Is/Ip and compare their similarity
-find the efficiency of the transformer using e = IsVs/IpVp