18.5.3Electric fields and capacitance (A Level)
Electric Potential Energy
5 min read 10 parts Lesson 11 of 19 1 quiz
Lesson summary
18.5.3 Electric Potential Energy — AS PHYSICS 9702 notes: Use Ep = QV and Ep = Q₁Q₂/(4πε₀r) and apply energy conservation to charges.Equation — Ep = QV, the work done bringing a charge Q from infinity to a point at potential VSign — Ep can be positive or negative since V can be e…
- Like charges
- System energy
- Zero at infinity
- Graph of Ep against r
- Work done by an external agent
- Moving away from a charge Q
Section 1 of 10Potential energy of a charge in a field
Equation
- Ep = QV, the work done bringing a charge Q from infinity to a point at potential V
Sign
- Ep can be positive or negative since V can be either
Like charges
- Like charges a positive charge near another positive charge has positive Ep because work was done against repulsion
Unlike charges
- Ep is negative, so they are bound and work is needed to separate them to infinity
Section 2 of 10Two point charges
Two point charges
Equation
- Ep = Q₁Q₂/(4πε₀r), found by putting the potential of Q₁ into Ep = Q₂V
- Do not square the distance
System energy
- System energy the energy is shared by the pair
Like charges
- Ep rises as r decreases
Unlike charges
- Ep becomes more negative as they approach
Zero at infinity
- Zero at infinity since V = 0 there, Ep = 0
Graph of Ep against r
- Graph of Ep against r a hyperbola, with force equal to minus its gradient, F = −dE_p/dr
Section 3 of 10Changes in potential energy
1Work done by an external agent
- W = QΔV = Q(V₂ − V₁), independent of the path
2Moving away from a charge Q
- ΔEp = qΔV = (Qq/4πε₀)(1/r₂ − 1/r₁)
3Free charges
- Free charges the change in Ep equals minus the change in kinetic energy if no other force acts
- A positive charge accelerates towards lower potential
4Work and the field
- Work and the field work is done on the field to bring like charges together or separate unlike charges, and by the field in the reverse cases
Section 4 of 10The electronvolt
Definition
- Definition the energy gained by an electron moving through a potential difference of one volt
Value
- 1 eV = 1.60 × 10⁻¹⁹ J
Charge 2e
- Charge 2e gains twice as many electronvolts through the same p.d.
Section 5 of 10Energy methods
1
Write down the initial and final energies, kinetic and potential
2
Use Ep = Q₁Q₂/(4πε₀r) for pairs, keeping the signs
3
Equate the total energy initially and finally if no energy is lost
4
Convert eV to J if needed
Closest approach
- Closest approach the projectile stops momentarily, so all its initial kinetic energy has become potential energy
- For a heavy fixed nucleus the energy given to the nucleus is negligible
Alpha scattering
- Alpha scattering this reasoning gave an upper limit of about 10⁻¹⁴ m for the size of the nucleus
Choice of zero
- Choice of zero only changes in energy matter in most problems
Section 6 of 10Comparison with gravity
Comparison with gravity
Gravitational potential energy
- Gravitational potential energy always negative relative to infinity because gravity only attracts
Analogy
- Analogy the rise in Ep as a negative charge moves away from a positive one is like lifting a mass on Earth
Electric case
- Electric case it can be positive or negative
Section 7 of 10Sign and direction checks
1Pushing like charges together
- Pushing like charges together the system gains energy, so the work done is positive
2Positive charge falling through a p.d. in the field direction
- Positive charge falling through a p.d. in the field direction it gains kinetic energy
3If the sign looks wrong
- If the sign looks wrong check the sign of ΔV
4Method
- Method write the energy statement in words first, then substitute numbers
Section 8 of 10More from the specification
More from the specification
Electric potential in radial fields
- The electric potential V at distance r from a point charge Q in vacuum is given by V = Q / , defined as work done per unit positive charge from infinity.
- (4 pi epsilon_0 r)
Electric potential energy between point charges
- The mutual potential energy of two point charges Q and q separated by distance r is Ep = Q q / .
- (4 pi epsilon_0 r)
Equipotential surfaces and field lines
- Equipotential surfaces run perpendicular to electric field lines;
- no work is done when a test charge is moved along an equipotential contour.
Field lines
- Lines showing the direction and strength of a magnetic field.
Permittivity
- A property of a medium affecting the electric force within it.
Radius
- Distance from the centre to the circular path.
Field strength
- G = Fg/m.
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Electric potential energy | work done bringing a charge from infinity, Ep = QV |
| Electronvolt | energy gained by an electron through 1 V, 1.60 × 10⁻¹⁹ J |
| Distance of closest approach | the separation at which a projectile stops momentarily |
| Bound pair | two opposite charges with negative potential energy |
| Conservation of energy | total kinetic plus potential energy is constant if no energy is lost |
| Work done by the field | the work the field does as a charge moves in it |
Section 10 of 10Exam technique
1
Squaring the distance in the potential energy equation — Ep varies as 1/r.
2
Using Ep = QV with the potential of the charge's own field — V is the potential due to the other charge.
3
Dropping signs of Q₁Q₂ — attractive pairs have negative Ep.
4
Forgetting to convert eV to joules.