9: motion in fields
DESCRIPTION
9: Motion in Fields. 9.3 Electrical field, potential and energy. Electric Fields Recap: Coulomb’s law : Electric field strength:. F = kQq r 2. …the force per unit charge experienced by a small positive point charge placed in the field. E = kQ r 2. Electrical Potential - PowerPoint PPT PresentationTRANSCRIPT
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9: Motion in Fields
9.3 Electrical field, potential and energy
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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
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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
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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
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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
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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.
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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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