Electromagnetism

The magnitude of the field will

• increase proportionally w/ the size of the charge

• decrease proportionally with the square of the distance

While grav. fields always exert an attractive force → electricity fields always exert an attractive or repulsive force

Electric field at a point →

• If FE = FG, the electron will move perfectly horizonatlly

Drawing electric fields

• goes from positive to negative

• positive out, negative in

Parallel Charges plates

Curve at the end

Electric fields

IN WHICH DIRECTION WOULD A POSITIVE TEST CHARGE EXPERIENCE A FORCE AT THAT POINT?

• Uniform electric fields have the same magnitude and direction at all points - e.g. between 2 parallel charged points

• in a field, you will experience a force without any contact between two objects

• can exert forces of attraction or repulsion

Particles in an electric field

• protons experience a force in the same direction as the field

• electron experiences a force in the opposite direction

• Electric field strength = force applied per coulomb of charge

• upward electric force and gravitational force can create net force = zero

• force between two charged particles is inversely proportional to the square of the distance between them

Coulomb’s Law

ONE COULOMB IS A HUGE CHARGE

The electric field emanating from a point charge will

• be proportional to the size of the charge

• be spherically symmetrical

• decrease in magnitude w/ increasing distance from the point charge

Defined using the 'ε₀’ permittivity of free space

• 1/(4πε₀) = 9×10^9 Nm² c^-2

Factors affecting the electric force

• proportional to product of the 2 charges

• regardless of the charge on each point, the forces on each point in a pair will be the same

Work and Electric Fields

• Electric field strength at a particular point = the force per unit charge that acts on a small positive test charge at that point.

• E = F/q or v/d

Electric potential energy

• a form of energy stored in an electric field

  • electric potentia at infinity is defined as zero

• Work can be done either

  • by the electric field on a charged object, reducing the electrical PE stored and increasing the KE of the object

  • on the electric field by forcing the object to move, thereby ⬆ electrical PE

Work done in electric fields

• if a charged object moves in the direction that it naturally tends to go within an electric field, work is done by the field.

  • When a positive point charge is moved in the direction of the electric field, the electric field does work on the point charge

• When work is done by a charged object on an electric field, the object is forced to move against its natural direction

  • work has been done on the field by forcing the object to move

Magnetic field lines

• show the direction of force acting on a magnetic north pole

• We can draw the magnetic field around an arrangement of magnets by determining the force that would act on a north pole at each point

  WHAT WOULD A NORTH MAGNETIC MONO-POLE DO?

• goes from North to south

• When N meets N → there will be a neutral point

Magnetic field sources

• created by a moving charge - even the magnetic field of a magnetic material (e.g. permanent magnet) is created by the motion of electrons w/in the atoms of the material

• In most materials, the magnetic fields created by the electrons cancel out such that there is no net magnetic field

• Only a few materials have an arrangement that allows for a net magnetic field - called ferromagnetic materials (e.g. iron, cobalt, nickel)

• A wire carrying a current will create a magnetic field

Calculating magnitude of the magnetic flux density

• permeability of free space = μ₀ = 1.25663706 × 10^-6 m kg s^-2 A^-2

• ^{conventional current = direction of positive charge = positive to negative}

  • from negative to positive over switch → increase in energy

Drawing magnetic fields → modification

• you can quickly determine where N is using a ‘modified’ right hand curl rule

  • if there is a loop of wire, curl fingers in direction of I, then thumb points in direction of N pole

Dipoles

• each end of a magnet is a magnetic pole, so when you break apart a magnet, each will form a separate magnet w/ 2 poles

  • therefore, they are dipolar

  • a magnetic field is a dipole field

• a suspended magnet that is free to move will always orientate itself in a north-south direction

• North and South Mag Poles ≠ North and South Pole

Magnetic Field lines

• produce fieds and will apply a force to objects made of ferromagnetic materials

• Run North to south external to the magnet, South to north inside the magnet/solenoid

• magnetic flux density/vector magnitude of mag. field @ a point is denoted by B and has units of T

• Perpendicular to current carrying wires

Magnetic fields between parallel wires

• If 2 wires are brought close together, their associated mag. fields will interact → resultant field = vector addition of each field

  • could attract/repel → when current is in the same direction: mag. fields are in opposite directions, reps. unlike poles, therefore wires attract

  • when current is in opposite direction, mag fields are in same direction and wires repel

3D Fields

• Lower density = weaker field

• As magnetic fields associated w/ current carrying coils are dependent upon the size of the current, a changing current will produce a changing mag. field

• Direction of current creates poles, poles can be reversed by reversing direction of the current

• magnetic flux density → can be changed by varying the amount of electric current that flows through it

Solenoids

• Many loops placed side by side, fields add together to produce a stronger effect

• Direction of a north solenoid can also be determined by using right hand grip rule in reverse. → curl fingers in direction of conventional current in wires, thumb points to north pole

• solenoids can be strengthened by wrapping coils around a soft iron core

  • forces atoms to align to one direction → ind. magnetic fields add together to create a stronger mag. field

Magnetic forces on charged particles

• a charged particle moving through a magnetic field will experience a force

  • particle must be travelling at right angles to the mag. field to maximise the force (angles <90 degrees still create a force)

• If a particle is moving in a direction that is perpendicular to the magnetic field, the speed of the particle will not change but its direction will - the particle will experience an acceleration (v. changed since direction has changed)

• ***for an object undergoing uniform circular motion w/ a radius orbit r, the Fc is present, therefore qvB = mv²/r

Particle Accelerators

• a synchrotron is a type of particle accelerator that constrains the motion of charged particles such that they move w/in large ring structures

• Charged particles → electrons and protons (therefore mass are charge are known)

• Radius of the curvatire → defined by the ring, so the velocity of the charged particles can be changed by changing the strength of the magnetic field

Right hand slap rule

• used to determine the direction of the force on a positively charged particle

  • the force on a negatively charged object will be in the opposite direction to that on a positively charged particle

Conductors in B fields

• If a conductor is in a magnetic field, and current is flowing throught the conductor, it will experience a magnetic force

• Still consider the direction of I and B

  • If I and B = parallel, there is no force

• Use right hand palm rule to determine direction of force but if force shows electrons, FLIP THUMB

Electric Motors

• A current carrying conductor will experience a force in a magnetic field

• We can use this principle to cause a coil of wire to notate in a magnetic field

  • To make it work, we need:

    • a power source (e.g. battery)

    • a permanent magnet/electromagnet

    • a coil of conducting material that can rotate in the B field

• Minimum torque will always be zero

• Max T → directly from IAnB

Commutators

• since current must be reversed at point when it will return to a point of rotational equilibrium

• allows direction to get reversed

• designed to feed current to the particular coil that is in the position to provide the max. torque

• split ring made of copper/another good conductor w/ conducting brushes (normally carbon blocks) rubbing against it

  • prevents wires from becoming tangled as coils rotate

Plotting F and T

Use graphs to plot force and Torque acting on one side of this electric motor

• 90 degrees typically corresponds to no force due to split ring

Torque

• turning force the coil experiences

• In a single square (rectangular coil) → total torque applied to coil will be twice acting on one side

  • forces = opposite but torque in same direction

Armature

whole arrangement of core and coils

Stator

permanent magnets that provide B (often stationary)

Practical motors

• have many coils w/ multiple turns

• commutators are used

• total torque = sum produced by every coil

• lithium-ion batteries → most common