1. 9.3 Electrical field, potential and energy
9: Motion in Fields
9.3 Electrical field, potential and energy

2. 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

3. Electrical Potential It can be shown that... or... V = kQ r V = 1 Q
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 = Q
4πε0 r

4. 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
E.g.

5. 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 = 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

6. 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

7. Equipotentials
Equipotential surfaces also exist in electric fields...

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9. 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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