Electric and Magnetic Fields

D2

Coloumb’s Law: Can be used to calculate the force between two charges

The relative permittivity εr for a medium other than a vacuum or air is defined as the ratio between the permittivity of the medium ε and the permittivity of free space ε₀:

Electric dipole positive and negative charge (has to be equal magnitude but opposite in sign)

Field strength is the amount of force per unit charge

Electric field:

• Points towards a negative charged and away from the positive charge, as it is defined based on what a small positive charge would do

• Electron moves in the opposite direction

• the total electric charge within an isolated system remains constant over time.

• Charge flows in between conductors until they have the same electric potential

Electric Potential:

• Represents electric potential energy per unit charge at any given point in space

• When two sphere are connected by thin wire they will end with same electric potential

• The work done to assemble a system from infinite separation

Electric potential difference (voltage):

• Difference in electric potential between two points

Solenoid:

• an electromagnetic device that converts electrical energy into linear mechanical motion

Electric Potential Energy:

• Represents the potential energy a particle has due to its position in a electric field

Electric Field Strength:

• the electrostatic force per unit charge exerted on a small positive test charge at any given point in space

Charge separation:

• It is the uneven distribution of positive and negative electric charges in a system

Parallel Plates:

• Are positively and negatively charged plates separated at some distance

• The electric field between a parallel plate is always constant, therefore the force is always constant

• Field is uniform in the middle and the horizontal components cancel each other to form a vertical electric field

• However the electric fields become weaker and weaker and non uniform at edges

Milikan experiment:

• Figured out the elementary charge of an electron and its mass

• Found mass of the oil droplet then turned electric plates in order to reduce veloicty

Creation and destruction of magnetic fields:

• Move one pole of a magnet over the material many times.

• Place material in a strong magnetic field

• Pass a constant electric current through the material

• Can unmagnetized them by heating them above the curie temperature

• or Physically disrupt the aligned domains with force

Domain Theory:

• states all materials are made up of tiny regions or domains that act and behave as a mini-magnet inside the material. If they are aligned they will become magnetized if random they cancel each other out

Magnetic Field B:

• A Magnetic Field B is the region of space around a magnet where another magnet or magnetic material will experience a force.

• Is measured in Teslas

• A compass is designed and engineered to always follow the magnetic field lines and point towards the South pole of a magnet (Lines leaving north pole and entering the south pole

• Strength is determined by the density of field lines The field lines never touch or cross each other’

Hand Rules:

• Use right hand for current or positive charges

• Use your left hand for electron flow

• Current Carrying wire

  • Place the thumb in the direction of the electric current.

  • The direction of the magnetic field curls with your fingers.

• Solenoids

  • Curl fingers around the loops in the direction of the current.

  • Thumb will point to the North pole of the solenoid.

    
    

    
    

Field Lines:

• Always originate from positive charges and terminate at negative charges

• Number of lines is proportional to the charge

• Perpendicular to the charge surface

Electromagnetism:

• A current carrying wire will create a magnetic field of concentric circles surrounding the wire

• An electron current flowing away from you produces a magnetic field that circulates in a clockwise direction

• An electric current flowing towards you produces a magnetic field that circulates in a counter clockwise direction

Two assumptions of particle travel

• The mass or charge is moving at a very small and constant speed → ΔEK ≈ 0 J (therefore no change in EK)

• We are considering the work done by external agent (force) to maintain this very small speed (no net force)

Two Scenarios

• Positive and positive zero potential energy when infinite distance from each other as become closer potential energy increases

• However if positive and negative then also start at zero at infinite distance, however as you start closer starts gaining negative potential energy

Equipotential Surface:

• Surface where the electrical potential energy is the same

• Electric field does no work on it

• Between two oppositely charged parallel plates, the electric field is uniform and points from the positive plate to the negative plate.

• Equipotential surfaces are always perpendicular to the electric field.

• Therefore, between parallel plates, the equipotential surfaces are parallel to the plates.

Conducting Spherical Sphere:

• The electric field inside the conductor's cavity is zero

  Therefore, the electric potential is constant everywhere inside the shell.

  The potential inside is equal to the potential at the surface.

Conductor:

•  a material that allows electric charge or thermal energy to move freely through its atomic structure

Insulator:

• a material that strongly resists the free flow of electric charge and heat through its atomic structure

D3

Current Carrying wire:

• If current goes same direction then they attract because magnetic field opposite direction cancel each other and from otherside push them towards each other

• If current goes opposite direction then repel as magnetic field from same direction repel

• Magnetic field at P is always tangent to the circle around the wire.

• Start at the wire and imagine the circular field; at P, follow the circle in the clockwise/anticlockwise direction to get the arrow.

Karate Hand rule/ Lorentz Hand rule:

• Palm represents force that particle will experience

• Fingers points to current in the direction of Magnetic Field B

• Thumb points in the direction of current (right conventional, left electron flow) or velocity of particle

• Conventional current right hand electron flow current left hand

• Positive charge right hand negative charge left hand

  
  

Electron volt: energy acquired by an electron moving through a potential difference of 1.0 volts

$F=BIl\sin\left(\theta\right)$

θ refers to the angle between magnetic field and current

When two current-carrying wires are placed side-by-side, they will interact with each other based on the magnetic fields they’ve created.

Cathode Ray:

• A cathode ray tube is a glass tube evacuated so only small amount of gas remain inside, with a potential difference acros it

• Negative electrode is the cathode

• Positive electrode is the anode

How to Calculate E/M ratio:

• Determine the known velocity of the electron using both electric and magnetic fields → known as the velocity selector ( as it will not move in the y direction which can only happen at one specific velocity

• Turn off the magnetic field (use only E field in step 3)

• Determine the vertical displacement of the electron.

• Solve for the e/m ratio using mechanics equations.

Electric field is the negative of potential gradient graph

Equipotential lines:

Equipotentials are defined as locations where the electric potential or gravitational potential is constant.

Equipotential lines always cross electric field lines at right angles, and have no direction (scalar quantity).

In a current wire the distance between equipotential surfaces increases after each line

Potential V:

• If more than one charge contribute to the potential at a point P then total potential V is the sum of all the individual potentials: change V is a scalar quantity!

• This is why V_e becomes a non-zero value inside a hollow charged sphere, rather than cancelling towards zero like the electric field E (which is a vector quantity)

Sphere:

• Acts as a point charge (Q)

• E inversely proportional to r2

Solenoid:

• When you pass power it creates magnetic field

• Solenoid hand rule fingers is current thumb is pointing dirrection of magnetic field

Magnetic field:

• Only affects electrons when not at rest

Magnetic Flux

• Measure of total magnetic field passing through a given area (T m²)

Lorentz Force:

$F=qvB\sin\left(\theta\right)$

Electric push +magnetic sideways push on a charged particle

Electric part: $F=qE$ (force along the electric field)

Magnetic part: $F=qvB\sin\left(\theta\right)$ (force perpendicular to both vvv and BBB)