# ELECTRIC FIELDS

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• Created by: CPev3
• Created on: 22-02-21 12:12

## Presence/ strength of an electric field?

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

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## Electric field strength

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

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## Electric field lines (lines of force)

• 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
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## Uniform electric field

• Electric field lines are parallel and equally spaced

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• Electric field strength is the same everywhere
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Electric field strength decreases with distance from the centre of the point charge

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## Coulomb's law

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 / 4πεo

F = Qq / 4πεor2

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## Presence/ strength of an electric field?

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

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E = F / q

= Qq / 4πεor2q

= Q / 4πεor2

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## Graph of E against 1 / r^2

• Straight line

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• Through the origin

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• Gradient = Q / 4πεo
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## Property that creates the field

Gravitational field

• Mass

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Electric field

• Charge
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## Type of field produced

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
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## Field strength

Gravitational field

• Force per unit mass
• g = F / m

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Electric field

• Force per unit positive charge
• E = F / Q
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## Force between particles

Gravitational field

• Force ∝ product of masses
• Force ∝ 1 / separation2

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Electric field

• Force ∝ product of charges
• Force ∝ 1 / separation2
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## Force and field strength equations

Gravitational field

• F = - GMm / r2
• g = - GM / r2

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Electric field

• F = Qq / 4πεor2
• E = Q / 4πεor2
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## Type of field

Gravitational field

• Point masses produce a radial field

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Electric field

• Point charges produce a radial field
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## Uniform electric field strength

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

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## Capacitance of a parallel-plate capacitor

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

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C = εoA / d, where εo = 8.85 x 10-12 Fm-1

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

......= εr (relative permittivity) x εo (permittivity of free space)

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

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## Electron between two parallel plates

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

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• E = V / d

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• F = EQ = Ee

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• W = Vq = Ve
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## Motion perpendicular to an electric field

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
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## Graph of F against r

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• Shows that F ∝ 1 / r2

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• Area = work done
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E = Qq / 4πεor

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