Chapter 17
Electric Potential
y2
q
y1
E
Topics in Chapter 17 – I: Basics
• Electric Potential Energy and Potential Difference
• Relationship between Potential and Electric Field
• Equipotential Lines or Surfaces
• The Electron Volt, a Unit of Energy
• Potential Due to Point Charges
• Potential Due to Electric Dipole; Dipole Moment
Electrostatic Potential Energy and Potential Difference
The electrostatic force is conservative – potential energy can be defined
Change in electric potential energy is the negative of work done by the electric force:
d
b
W = Fd d = da b || E
Electrostatic Potential Energy and Potential Difference
Basic Definition: Electric potential is defined as potential energy per unit (test) charge: For ‘test’ q at location a we have
Unit of electric potential: the volt (V).
1 V = I J/C.
Electrostatic Potential Energy and Potential Difference
Only differences in potential can be measured, allowing free assignment of V = 0.
Electrostatic Potential Energy and Potential Difference
Analogy between gravitational and electrical potential energy:
Relation between Electric Potential and Electric Field
Work is charge multiplied by potential difference:
Work is also force multiplied by distance:
Here d is the distance along the field direction.
Relation between Electric Potential and Electric Field
Solving for the (uniform) electric field, || E
If the field is not uniform, it can be calculated point by point using
Ey = − ∆V/∆y etc
Equipotential Lines or Surfaces
An equipotential is a line or surface over which the potential is constant.
Electric field lines are perpendicular to equipotentials. The surface of a conductor is an equipotential. (For static case, the whole conductor is at the same electrostatic potential.)
The Electron Volt, a Unit of Energy
One electron volt (eV) is the energy gained by an electron moving through a potential difference of one volt.
Energy gained by acceleration due to electric force
Is equal to the Work done W = qEd = q(∆V)
Electric Potential Due to a Point Charge
The electric potential due to a point charge can be derived ­ but that uses calculus.
Natural V = 0 for point charges is infinite r
Remember that V is a scalar ­ it has no direction.
r is the distance from Q to observation point.
Electric Potential Due to Point Charges
Positive Q
Negative Q
These plots show the potential due to (a) a positive charge and (b) a negative charge.
Using potentials instead of fields can make problems easier – Remember that the potential is a scalar, but the field is a vector.
Equipotential Lines
Electric dipole
Potential Due to Electric Dipole; Dipole Moment
The potential due to an electric dipole is just the sum of the potentials due to each charge, and can be calculated exactly.
V = ΣQ Vdue to Q = V+ + V−
Can extend this idea to any problem with multiple point charges. Potential is a simple (scalar) sum of the potential due to the individual source charges.
Potential Due to Electric Dipole; Dipole Moment
Look at the details to develop the approximation for potential far from an electric dipole: r >> l
r­
Result is
Dipole moment: p = Ql r+
Topics in Chapter 17 ­ II
• Capacitance
• Dielectrics
• Storage of Electric Energy
Capacitors
A capacitor is made up of two conductors separated by a small insulating gap and can store charge a) parallel­plate capacitor connected to battery. b) is a circuit diagram.
Capacitance
When a capacitor is connected to a battery, the charge on its plates is proportional to the voltage:
The quantity C is called the capacitance. It depends only on the materials used and geometry factors.
Unit of capacitance: the farad (F) C = Q / V
1 F = 1 C/V
Capacitance
The capacitance does not depend on the voltage; it depends on geometry and material of the capacitor.
For a parallel­plate capacitor:
This will be different for other geometries.
Dielectrics
A dielectric is an insulator, and is characterized by a dielectric constant K. Usually K > 1
Capacitance of a parallel­plate capacitor filled with dielectric:
For any equation that is applied inside a dielectric material substitute K for Dielectrics
Dielectric strength is the maximum field a dielectric can experience without breaking down.
The dielectric constant and breakdown field determine which dielectric materials are best for a given use.
Dielectrics
The molecules in a dielectric tend to become oriented in a way that reduces the external field.
This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential.
Storage of Electric Energy
A charged capacitor stores electric energy. The energy stored is equal to the work done to charge the capacitor.
For a parallel plate capacitor with vacuum the constant electric field inside is E = V/d = Q/A
The PE is “stored” in the electric fields. Storage of Electric Energy
The energy density, defined as the energy per unit volume, is the same no matter the origin of the electric field:
Do the algebra to show this result for parallel plates.
The sudden discharge of electric energy can be harmful or fatal. Capacitors can retain their charge indefinitely even when disconnected from a voltage source – be careful!
Cathode Ray Tube: TV and Computer Monitors, Oscilloscope
The electrons can be steered using electric fields.
Summary of Chapter 17
• Electric potential energy:
• Electric potential difference: work done to move charge from one point to another
• Relationship between potential difference and field:
Summary of Chapter 17
• Equipotential: line or surface along which potential is the same
• Electric potential of a point charge:
• Electric dipole potential:
Summary of Chapter 17
• Capacitor: nontouching conductors carrying equal and opposite charge
• Capacitance:
• Capacitance of a parallel­plate capacitor:
Summary of Chapter 17
• A dielectric is an insulator
• Dielectric constant gives ratio of total field inside the material to the external field
• Energy density in an electric field: