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9: Motion in Fields

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9: Motion in Fields

9.3 Electrical field, potential and energy

Electric Fields

Recap:

Coulomb’s law:

Electric field strength:

F = kQq r2

…the force per unit charge experienced by a small positive point charge placed in the field.

E = kQ

r2

Electrical Potential

It can be shown that...

or...

Where... V = Electrical potential (Volts or JC-1)

r = distance from centre of point charge (m)

Q = point charge (Coulombs)

k = Coulomb constant = 8.99 x 109 Nm2 C−2

The electrical potential at a point in a field is defined as the work done per unit charge in bringing a positive test charge from infinity to the point in the field.

V = kQ

r

V = 1Q

4πε0 r

E.g.

Calculate the potential due to the proton in a hydrogen atom at a distance 0.5 x 10-10m.

( k = 8.99 109 N m2 C-2 )

A: V= 29V

Electric Potential Energy

Again it can be shown that...

or...

The electrical potential energy of a point charge at any point is defined as the work done in moving the charge from infinity to that point.

Ep = kQq

r

Ep = 1Qq

4πε0 r

E.g. Calculate the potential energy between the proton in a hydrogen atom and an electron orbiting at radius 0.5 x 10-10m.

( k = 8.99 109 N m2 C-2 )

A: E = -46 x 10-19J

Work done moving a charge

If a charge is moved from one point (x) to another (y), where the potential is different, work is done.

Work done = Final Ep – Initial Ep

= Vyq - Vxq

The path taken does not affect the work done.

Work done will equal the change in potential energy.

x

y

Equipotentials

Equipotential surfaces also exist in electric fields...

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Potential gradient

Again, this will be equal to the field strength at a point in an electrical field...

Work done to move a charge from one potential to another = qΔV

But also W = FΔx

So... FΔx = qΔV

So...

E = (-) ΔV

Δx

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