🧲AP Physics 2 (2025) Unit 10 – Electric Force, Field, and Potential

Key Concepts and Definitions

• Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field
• Electric force is the attractive or repulsive interaction between electrically charged particles
• Electric field is a region around an electric charge in which an electric force is exerted on another charge
• Electric potential energy is the energy that is needed to move a charge against an electric field
• Voltage, or electric potential difference, is the difference in electric potential energy per unit charge between two points
• Coulomb's law states that the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them
• Permittivity is a measure of how much resistance is encountered when forming an electric field in a particular medium
  • Permittivity of free space ($\varepsilon_0$) is a constant equal to $8.85 \times 10^{-12}$ $\text{F}/\text{m}$

Fundamental Laws and Equations

• Coulomb's law: $F = k \frac{|q_1 q_2|}{r^2}$, where $F$ is the electric force, $k$ is Coulomb's constant ($8.99 \times 10^9 \text{N} \cdot \text{m}^2/\text{C}^2$), $q_1$ and $q_2$ are the magnitudes of the charges, and $r$ is the distance between the charges
• Electric field strength: $E = \frac{F}{q}$, where $E$ is the electric field strength, $F$ is the force exerted on a test charge, and $q$ is the magnitude of the test charge
• Electric potential energy: $U = qV$, where $U$ is the electric potential energy, $q$ is the charge, and $V$ is the electric potential (voltage)
• Electric potential (voltage): $V = \frac{U}{q} = \frac{W}{q}$, where $V$ is the electric potential, $U$ is the electric potential energy, $q$ is the charge, and $W$ is the work done to move the charge
• Electric field and potential relationship: $E = -\frac{\Delta V}{\Delta s}$, where $E$ is the electric field strength, $\Delta V$ is the change in electric potential, and $\Delta s$ is the displacement
• Gauss's law: $\Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}$, where $\Phi_E$ is the electric flux, $\vec{E}$ is the electric field, $d\vec{A}$ is the area element, $Q_{\text{enc}}$ is the enclosed charge, and $\varepsilon_0$ is the permittivity of free space

Electric Charge and Its Properties

• Electric charge is quantized, meaning it comes in discrete units (multiples of the elementary charge, $e = 1.602 \times 10^{-19}$ C)
• Charge is conserved in an isolated system, meaning the total charge remains constant
• Like charges repel each other, while unlike charges attract each other
• Charge can be transferred through conduction (direct contact) or induction (redistribution of charge without contact)
• Insulators are materials that do not allow charge to flow easily (glass, rubber, plastic)
• Conductors are materials that allow charge to flow easily (metals, graphite, salt water)
  • Charges on a conductor will distribute themselves evenly on the surface
• Polarization occurs when an electric field causes a separation of positive and negative charges within an object

Electric Force and Coulomb's Law

• Coulomb's law describes the force between two point charges
  • The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them
• The electric force is a conservative force, meaning the work done by the force is independent of the path taken
• The electric force is a long-range force, meaning it can act over large distances
• The direction of the electric force depends on the signs of the charges
  • Like charges (both positive or both negative) repel each other
  • Unlike charges (one positive, one negative) attract each other
• The magnitude of the electric force decreases rapidly with distance, following an inverse square law
• Coulomb's law can be used to calculate the force between multiple point charges by using the superposition principle (adding the individual forces as vectors)

Electric Fields: Concept and Calculations

• An electric field is a region in which an electric charge experiences a force
• The electric field strength at a point is defined as the force per unit charge on a positive test charge placed at that point
• The direction of the electric field at a point is the direction of the force on a positive test charge placed at that point
• Electric field lines are used to visualize the electric field, with the direction of the field line indicating the direction of the force on a positive charge
  • Field lines start on positive charges and end on negative charges
  • The density of field lines indicates the strength of the electric field
• The electric field due to a point charge can be calculated using Coulomb's law and the definition of electric field strength
• The electric field due to multiple point charges can be calculated using the superposition principle (adding the individual fields as vectors)
• The electric field inside a conductor is zero, as the charges redistribute themselves to cancel out the field

Electric Potential and Voltage

• Electric potential, or voltage, is the potential energy per unit charge
• The electric potential difference between two points is the work required to move a unit positive charge from one point to the other
• The electric potential is a scalar quantity, while the electric field is a vector quantity
• The electric potential is always defined relative to a reference point (usually taken to be infinity, where the potential is zero)
• The electric potential due to a point charge can be calculated using the electric potential energy equation and the definition of electric potential
• The electric potential due to multiple point charges can be calculated using the superposition principle (adding the individual potentials)
• Equipotential surfaces are surfaces on which all points have the same electric potential
  • Equipotential surfaces are always perpendicular to electric field lines
• The relationship between electric field and electric potential is given by $E = -\frac{\Delta V}{\Delta s}$, where $E$ is the electric field strength, $\Delta V$ is the change in electric potential, and $\Delta s$ is the displacement

Applications and Real-World Examples

• Van de Graaff generators use electric fields to accumulate charge on a large metal sphere, creating high voltages (used in particle accelerators, electrostatic precipitators)
• Electrostatic precipitators use electric fields to remove particulate matter from exhaust gases (power plants, industrial facilities)
• Capacitors store electric charge and energy in an electric field between two conducting plates (electronic circuits, power supplies)
• Lightning occurs when the electric field in the atmosphere exceeds the dielectric strength of air, causing a rapid discharge of electricity (thunderstorms)
• Electrostatic painting uses an electric field to attract charged paint particles to a grounded object (automotive industry, appliance manufacturing)
• Xerography (photocopying) uses electric fields to transfer toner particles onto paper (office equipment, printing)
• Electrostatic separation is used to separate materials based on their electrical properties (recycling, mineral processing)

Common Problem-Solving Strategies

• Identify the given information and the quantity to be calculated
• Draw a diagram of the situation, including charges, forces, fields, and distances
• Determine the appropriate equation or principle to use based on the given information and the quantity to be calculated
• Substitute the given values into the equation and solve for the unknown quantity
• Check the units of the answer to ensure they are consistent with the quantity being calculated
• Verify that the answer makes sense in the context of the problem (sign, magnitude, direction)
• When dealing with multiple charges, use the superposition principle to calculate the total force, field, or potential
• When working with electric fields and potentials, consider symmetry and geometry to simplify calculations (e.g., using Gauss's law for symmetric charge distributions)
• Break down complex problems into smaller, more manageable steps
• Double-check calculations and reasoning to avoid errors and misconceptions