Electrical Fields

Field Patterns

• Electrical conductors contain lots of free electrons

• Electrical insulators contain no free electrons

Any two charged objects exert an equal and opposite force on each other without being in contact

• Field lines are the direction that a positive test mass will follow if placed in the field

Electrical Field Strength

• A charged object in an electric field experiences a force due to the field.

• E (electric field strength) at a point is the force per unit charge on a positive test charge placed at that point (N/C)

E=F/Q

Between 2 parallel plates

• field lines are parallel

• field lines are at right angles to the plates

• field lines go from positive to negative

• The FIELD IS UNIFORM. (E has the same magnitude and direction everywhere between the plates)

E = V/d

Field Factors

• Increase charge near a body = increase E

• If the body is metal - charge is spread across the surface

Electric Potentials

• Work must be done to move a charged object X to another charged object Y (if they have the same type of charge) - so their Electric Potential Energy increases as X moves towards Y

Electric potential (V) = the work done per unit positive charge on a positive test charge when it is moved from infinity to that position, where at infinity, V=0.

V = E_p/Qv

ΔW = mΔV (where Δv = V2-V1)

Potential Gradients

• Equipotentials are surfaces of constant potential

• Test charges moving across an equipotential have constant E_p

• The field lines cross equipotentials at right angles - so no work is done by the electric field on the test charge

Potential Gradient = change of potential per unit charge of distance in a given direction

1) Non uniform field = Potential gradient will vary (the closer the equipotentials are, the greater the potential gradient is)

2) Uniform Field = potential gradient is constant (the equipotentials between the plates are evenly spaced lines parallel to the plates. ALSO - POTENTIAL INCREASES IN THE OPPOSITE DIRECTION TO THE NEGATIVE FIELD

E is equal to the negative of the potential gradient

E = -ΔV/Δd

E = QK/A = QK/r²

Point charges

• If point charges have forces acting in the same direction

• E_T = E₁ + E₂

• If point charges have forces acting in opposite directions

• E_T = E₁ - E₂

• If at right angles, use pythagoras