Electric Potential Energy and Potential Difference

Electrostatic Force and Potential Energy

The electrostatic force is a conservative force, which means that potential energy can be defined for a system of charges. The change in electric potential energy is the negative of the work done by the electric force:

• Equation:

• Electric potential is defined as potential energy per unit charge:

• Unit of electric potential: The volt (V), where .

• Only changes in potential can be measured, allowing free assignment of .

• Equation for potential difference:

• Analogy: Just as a more massive rock has more gravitational potential energy, a larger charge has more electrical potential energy.

Relation between Electric Potential and Electric Field

Work, Potential, and Electric Field

Work done by or against electric forces can be expressed in terms of potential or field:

• Work as charge multiplied by potential:

• Work as force multiplied by distance:

• Electric field from potential difference: (for uniform )

• In general, the electric field at any point is equal to the rate at which the electric potential decreases over distance in that direction.

Equipotential Lines and Surfaces

Properties and Applications

An equipotential is a line or surface over which the potential is constant. These are useful for visualizing electric fields and potentials.

• Electric field lines are always perpendicular to equipotential lines/surfaces.

• The surface of a conductor is an equipotential.

• Equipotential lines for an electric dipole show symmetry and help in understanding field distributions.

The Electron Volt, a Unit of Energy

Definition and Conversion

The electron volt (eV) is a convenient unit of energy in atomic and nuclear physics.

• One electron volt is the energy gained by an electron moving through a potential difference of one volt.

• Conversion:

Electric Potential Due to Point Charges

Formulas and Graphs

The electric potential due to a point charge is derived using calculus and is a fundamental result in electrostatics.

• Equation:

• For a positive charge, potential decreases with distance; for a negative charge, potential is negative and increases (less negative) with distance.

• Potential is a scalar quantity, making calculations simpler than using vector fields.

Potential Due to Electric Dipole; Dipole Moment

Exact and Approximate Solutions

The potential due to an electric dipole is the sum of the potentials from each charge. For points far from the dipole, an approximation is used:

• Approximate potential far from dipole:

• Defining the dipole moment :

Capacitance

Definition and Properties

A capacitor consists of two conductors separated by an insulator and can store electric charge.

• When connected to a battery, the charge on the plates is proportional to the voltage:

• Capacitance () is a property of the geometry and materials, not the voltage.

• Unit of capacitance: The farad (F), where .

• For a parallel-plate capacitor:

Dielectrics

Role and Effects

A dielectric is an insulating material characterized by its dielectric constant (). It increases the capacitance of a capacitor.

• Capacitance with dielectric:

• Dielectric strength is the maximum field a dielectric can withstand without breakdown.

• Molecules in a dielectric orient to reduce the external field, allowing more charge to be stored for the same potential.

Storage of Electric Energy

Energy in Capacitors

A charged capacitor stores electric energy, which is equal to the work done to charge it.

• Energy stored:

• Energy density:

• Capacitors can retain charge even when disconnected, and sudden discharge can be dangerous.

• Application: Heart defibrillators use electric discharge to restore normal heart rhythm.

Digital; Binary Numbers; Signal Voltage

Analog vs. Digital Signals

Signal voltages can be analog (continuous) or digital (discrete, binary).

• Analog signals vary continuously over time.

• Digital signals use binary numbers to represent values, making them less sensitive to noise.

• Conversion from analog to digital requires sampling; higher sampling rates yield more accurate digital representations.

• Digital audio signals must be converted back to analog before playback.

TV and Computer Monitors: CRTs, Flat Screens

Display Technologies

Monitors use different technologies to display images:

• Cathode Ray Tube (CRT): Contains a wire cathode that emits electrons when heated. Electrons are accelerated toward an anode and steered by electric or magnetic fields to create images on a fluorescent screen.

• Flat Screens: Use arrays of tiny pixels in red, green, and blue. The brightness of each pixel can be controlled to form images. High-definition screens have resolutions such as 1080 x 1920 pixels.

Electrocardiogram (ECG or EKG)

Medical Application of Electric Potential

The electrocardiogram detects heart defects by measuring changes in electric potential on the surface of the heart. This is an important application of electric potential in medicine.

• ECG signals are analyzed to diagnose heart conditions.

Summary of Key Equations

• Electric potential:

• Potential difference: (uniform field)

• Point charge potential:

• Capacitance:

• Parallel-plate capacitor:

• Capacitance with dielectric:

• Energy stored:

• Energy density:

Additional info: These notes expand on the original slides with definitions, examples, and applications for clarity and completeness.