ELECTRIC FIELDS

Positively charged metal ball

Attach a piece of gold foil to the bottom of an insulator

Tap the ball with the foil

The foil will be given a constant positive charge

Bring the foil close to the ball

The foil will experience an electrostatic force

↑ distance = weaker electric field = smaller electrostatic force

Force experienced per unit positive charge

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E = F / Q

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Vector quantity (has both magnitude and direction)

Direction of electric field = direction in which a positive charge would move

• Map electric field patterns

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• Arrow shows the direction of the field

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• Perpendicular to the surface of a conductor

• Electric field lines are parallel and equally spaced

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• Electric field strength is the same everywhere

Electric field strength decreases with distance from the centre of the point charge

Any two point charges exert an electrostatic force on each other

......that is directly proportional to the product of their charges

............and inversely proportional to the square of their separation

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F = kQq / r²

k = 1 / 4πε_o

F = Qq / 4πε_or²

Two table-tennis balls coated in conductive paint

Tap the positive electrode of a high-tension supply with both balls

The balls will be given a constant positive charge

Attach each ball to the bottom of an insulating rod

Balance one rod on a sensitive top-pan balance

Lower the other rod

↑ distance = smaller reading on the balance

E = F / q

= Qq / 4πε_or²q

= Q / 4πε_or²

• Straight line

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• Through the origin

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• Constant, positve gradient

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• Gradient = Q / 4πε_o

Gravitational field

• Mass

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Electric field

• Charge

Gravitational field

• Always attractive

• Direction of field always towards object

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Electric field

• Positive point charges produce a repulsive field
  • Direction of field away from object
  • Repels a positive charge

• Negative point charges produce an attractive field
  • Direction of field towards object
  • Attracts a positive charge

Gravitational field

• Force per unit mass

• g = F / m

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Electric field

• Force per unit positive charge

• E = F / Q

Gravitational field

• Force ∝ product of masses

• Force ∝ 1 / separation²

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Electric field

• Force ∝ product of charges

• Force ∝ 1 / separation²

Gravitational field

• F = - GMm / r²

• g = - GM / r²

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Electric field

• F = Qq / 4πε_or²

• E = Q / 4πε_or²

Gravitational field

• Point masses produce a radial field

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Electric field

• Point charges produce a radial field

W = Fd

W = VQ and F = EQ

∴ VQ = EQd

so V = Ed or E = V / d

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1 NC^-1 = 1 Vm^-1

For plates in a vacuum/ air, C ∝ A / d

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C = ε_oA / d, where ε_o = 8.85 x 10^-12 Fm^-1

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ε (permittivity of dielectric (excluding a vacuum/ air))

......= ε_r (relative permittivity) x ε_o (permittivity of free space)

∴ for plates separated by a dielectric other than a vaccuum/ air, C = εA / d

Uniform electric field between the plates

Electron is negatively charged

Travels

• away from the negative plate
• towards the positive plate
• in the opposite direction to the electric field

Experiences a constant electrostatic force

Constant acceleration

• E = V / d

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• F = EQ = Ee

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• W = Vq = Ve

Path is parabolic

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Horizontal motion

• a is zero

• u and v are constant

• t = L / v, where L is the horizontal distance

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Vertical motion

• a = F / m = EQ / m

• u is zero

• v = u + at = 0 + (EQ / m) x (L / v) = EQL / mv

• Changing, negative gradient

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• Shows that F ∝ 1 / r²

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• Area = work done

E = Qq / 4πε_or