9: Motion in Fields

9.3 Electrical field, potential and energy

Electric Fields

Recap:

Coulomb’s law:

Electric field strength:

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

F = kQq r2

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 = 1 Q 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 = 1 Qq 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

x

y

The path taken does not affect the work done.Work done will equal the change in potential energy.

Equipotentials

Equipotential surfaces also exist in electric fields...

Subtitle

Text

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

Subtitle

Text

Subtitle

Text

Subtitle

Text

Subtitle

Text

Subtitle

Text

Subtitle

Text

Subtitle

Text

Subtitle

Text

Subtitle

Text

Subtitle

Text

Subtitle

Text

Subtitle

Text