Electric fields

What creates an electric field around it?

charged object

Electric field defintion:

Region where an electric charge experiences a force

What is a point charge?

For a point outside a spherical conductor, the charge of the sphere may be considered to be a point charge at its centre

electric field lines around a spherical conductor are ____ to those around a point charge

same

example of a spherical conductor is a ________

charged sphere

Field lines:

• Radial

• Go towards centre of a conductor

• Pos —> neg

direction of electric fields is represented by

electric field line

uniform electric field has the same ______ throughout the field

electric field strength

how to represent uniform electric field?

equally spaced field lines

stronger field is represented by the field lines ____

are closer together

radial field is considered a ______ field

non-uniform

electric field strength definition:

electrostatic force per unit positive charge acting on the charge at that point

units of electric field strength

V m⁻¹ or N C⁻¹

What equation shows magnitude of the electric field strength in a uniform field between two charged parallel plates:

E= V/d

What can equation not show?

cannot be used to find the electric field strength around a point charge (since this would be a radial field

direction of the electric field is from the plate connected to the positive terminal of the cell to the plate connected to the negative terminal

How does potential difference form in field?

two points in electric field have different potential

When a charge moves across a p.d what happens?

Work is done

P.d. defintion

energy transfered per unit charge

V= W/Q

Remember

equation for electric field strength with V and d is only for parallel plates and not point charge (use E=F/Q)

Coulomb’s law

The electrostatic force between two point charges is proportional to product of charges and invesly prop to square of seperation

e.g. F-=Qq/4 Pie E0 r2

What units mean in :

F= electrostatic force (N)

Q,q= magnitudes of charges (C)

r= distance between centres of two charges (m)

ε₀ = permittivity of free space

what is value for permittivity of air?

taken to be the same as ε0

Coulomb's law can only be applied to charged spheres whose size is much smaller than their separation. Only in this case, the point charge approximation is valid. You must remember that the separation r must be taken from the centres of the spheres.

cannot use Coulomb's law to calculate the electrostatic force between charges distributed on irregularly-shaped objects.

a point charge produces a ____ field

radial

What equation is used to find electric field strength E at distance r to point charge Q in free space:

units:

Q- point charge producing the radial electric feild (C)

r- distance from centre of charge (m)

ε0 = permittivity of free space (F m−1)

what does this equation show:

• Electric field strength in radial field is not constant

• As distance from charge increase, E decreases by factor 1/r2

What is permittivity?

measure of how easy it is to generate an electric field in a certain material

What is a dielectric constant?

relativity of permittivity ε_r

relativity of permittivity ε_r

The ratio of the permittivity of a material to the permittivity of free space

equation of Er (learn):

• Where:

  • ε_r = relative permittivity

  • ε = permittivity of a material (F m⁻¹)

  • ε₀ = permittivity of free space (F m⁻¹)

What happens when the polar molecules in a dielectric (poor conductor of electricity but good supporter of electric fields) align with the applied electric field from the plates?

each produce own electric field, which opposes electric field from plates

larger opposing electric field from the polar molecules in the dielectric= larger permittivity

opposing electric field reduces the overall electric field, which decreases the potential difference between the plates

Therefore, the capacitance of the plates increases

units:

C = capacitance (F)

A = cross-sectional area of the plates (m2)

d = separation of the plates (m)

εr = relative permittivity of the dielectric between the plates

ε0 = permittivity of free space (F m−1)

charged particle in an electric field will experience a ____ on it that will cause it to ____

force

move

if a charged particle remains still in a uniform electric field

move parallel to the electric field lines (along or against the field lines depending on its charge

If a charged particle in motion travels initially perpendicular through a uniform electric field:

constant electric force and travel in a parabolic trajectory

What direction will charge move?

• positive charge will be deflected towards the negative plate

• negative charge will be deflected towards the positive plate

force on the particle is the same at all points and is always in the same direction

how will uncharged particle act in electric field?

travel straight through the plates undeflected

amount of deflection depends on the following properties of the particles:

• Mass – the greater the mass, the smaller the deflection and vice versa

• Charge – the greater the magnitude of the charge of the particle, the greater the deflection and vice versa

• Speed – the greater the speed of the particle, the smaller the deflection and vice versa

electrostatic field definition:

electric force per unit charge exerted on a small positive test charge

Radial fields always have an inverse square law relationship with distance

Equipotential surfaces for both gravitational and electric fields are spherical around a point mass or charge and equally spaced parallel lines in uniform fields

when drawing field lines:

• electric FL always at right angle to surface of conductor

• increased field strength = lines closer together

we consider a charge a point charge if:

• separation of object is greater than size of object

• if charge doesn’t affect electric field its in

Motion of particle

Electric field strength- E=V/d

Force on charged particle- F=EQ (=Ee for electrons)
Work done by particles- W=Vq

• When particle travels at right angle to electric field, motion is parabolic path

• Horizontal- no a, t=L/v

• Vertical- a=F/m= EQ/m

  Vv= u+ at

  = 0 + (EQ/m)(L/v)

particle accelerators:

• Electron beam usually produced in vacuum tube by thermionic emission from heated cathode

• Electrons are accelerated from cathode (-) and anode (+) with small hole in it which allows some electrons through

• electrons are focused into beam by further electrodes + coils

• electron leaves hot cathode with horizontal acceleration

• in uniform electrostatic field, beam is deflected in similar way to mass projected horizontally in earths gravitational field

• linear accelerator consists of long series of electrodes connected alternately to a source of alternating p.d

• electrodes are hollow coaxial cylinders in long evacuated tube

• charged particles released at one end of tube are accelerated to nearest electrode which they pass through as alternating p.d. reverses polarity

• particles then repelled on leaving this electrode and are attracted to next electrode, so that charged particles gain KE each time they pass between electrons

If a charge is to move with an electric field

field does work on charge

If charge is to move against the field

work must be done on charge

equation to learn

V=W/Q

Electric potential= electric potential energy/ Q

Features of Force against separation graph:

shows Columbus law

AREA= work done

Total work done= EPE ∴ E=Qq/4 PIE E0 r (between 2 charges)

equation for EP:

V=Q/4 PIE E0 r

If we say Fr=Work done what do we assume?

F is constant

deflection is related to …

force

definition of electrical potential at point in space:

work done per unit charge in bringing a positive charge from infinity to a point