Electric Field Formulas to Know for AP Physics 2

Understanding electric fields is key in electromagnetism. These formulas explain how charges interact, create fields, and store energy. From Coulomb's Law to capacitance, these concepts are essential for grasping the behavior of electric forces and potentials in various scenarios.

1. Coulomb's Law: F = k(q1q2)/r²

   • Describes the force between two point charges.
   • Force is directly proportional to the product of the charges (q1 and q2).
   • Force is inversely proportional to the square of the distance (r) between the charges.
   • k is Coulomb's constant, approximately 8.99 x 10⁹ N m²/C².
   • The force can be attractive or repulsive depending on the signs of the charges.

2. Electric field due to a point charge: E = kq/r²

   • Defines the electric field created by a single point charge (q).
   • The electric field (E) points away from the charge if it is positive and towards it if negative.
   • The strength of the electric field decreases with the square of the distance (r) from the charge.
   • k is the same Coulomb's constant used in Coulomb's Law.
   • Units of electric field are N/C (Newtons per Coulomb).

3. Electric field due to a dipole: E = kp/(4πε₀r³)

   • Describes the electric field generated by an electric dipole, which consists of two equal and opposite charges separated by a distance (p).
   • The field strength decreases with the cube of the distance (r) from the dipole.
   • ε₀ is the permittivity of free space, approximately 8.85 x 10⁻¹² C²/(N m²).
   • The dipole moment (p) is a measure of the separation of positive and negative charges.
   • Important in understanding molecular interactions and polar molecules.

4. Superposition principle for electric fields

   • States that the total electric field created by multiple charges is the vector sum of the individual fields.
   • Each charge contributes to the electric field independently.
   • Allows for the analysis of complex charge configurations.
   • Important for solving problems involving multiple point charges.
   • Vector addition must consider both magnitude and direction.

5. Electric field due to an infinite line charge: E = λ/(2πε₀r)

   • Describes the electric field generated by an infinitely long line of charge with linear charge density (λ).
   • The electric field is directed radially outward from the line charge.
   • The strength of the electric field decreases linearly with distance (r) from the line.
   • Useful in applications involving charged wires or filaments.
   • Units of λ are C/m (Coulombs per meter).

6. Electric field due to an infinite plane of charge: E = σ/(2ε₀)

   • Defines the electric field produced by an infinite plane with uniform surface charge density (σ).
   • The electric field is constant and does not depend on the distance from the plane.
   • The field points away from the plane if the charge is positive and towards it if negative.
   • Important in capacitor design and understanding field behavior in charged surfaces.
   • Units of σ are C/m² (Coulombs per square meter).

7. Electric field inside a conductor: E = 0

   • States that the electric field inside a perfect conductor in electrostatic equilibrium is zero.
   • Charges redistribute themselves on the surface of the conductor to cancel any internal field.
   • Important for understanding shielding effects and electrostatic conditions.
   • No net electric field means no work is done on charges inside the conductor.
   • Applies to static situations; dynamic conditions may differ.

8. Gauss's Law: ∮E⋅dA = Q/ε₀

   • Relates the electric field (E) over a closed surface to the charge (Q) enclosed by that surface.
   • The left side represents the electric flux through the surface.
   • Useful for calculating electric fields in symmetric charge distributions.
   • ε₀ is the permittivity of free space.
   • Highlights the relationship between charge and electric field in a clear mathematical form.

9. Electric potential energy: U = kq1q2/r

   • Defines the potential energy (U) between two point charges.
   • Potential energy is positive for like charges (repulsion) and negative for unlike charges (attraction).
   • Depends on the distance (r) between the charges and the magnitudes of the charges.
   • Important for understanding energy conservation in electric fields.
   • Units of potential energy are Joules (J).

10. Electric potential: V = kq/r

    • Describes the electric potential (V) at a point in space due to a point charge (q).
    • Electric potential is a scalar quantity and represents the potential energy per unit charge.
    • The potential decreases with increasing distance (r) from the charge.
    • Important for calculating work done in moving charges within an electric field.
    • Units of electric potential are Volts (V).

11. Relationship between electric field and potential: E = -∇V

    • Indicates that the electric field (E) is the negative gradient of the electric potential (V).
    • Shows how electric fields point in the direction of decreasing potential.
    • Important for understanding how potential differences drive current in circuits.
    • The relationship is fundamental in electrostatics and field theory.
    • Highlights the connection between force and energy in electric fields.

12. Capacitance: C = Q/V

    • Defines capacitance (C) as the ratio of charge (Q) stored to the potential difference (V) across a capacitor.
    • A measure of a capacitor's ability to store electric charge.
    • Units of capacitance are Farads (F).
    • Higher capacitance means more charge can be stored for a given voltage.
    • Important in circuit design and energy storage applications.

13. Parallel plate capacitor: C = ε₀A/d

    • Describes the capacitance of a parallel plate capacitor, where A is the area of the plates and d is the separation between them.
    • The capacitance is directly proportional to the area and inversely proportional to the distance between the plates.
    • ε₀ is the permittivity of free space, affecting the capacitor's ability to store charge.
    • Important for understanding basic capacitor behavior in circuits.
    • Used in various electronic applications for energy storage.

14. Energy stored in a capacitor: U = ½CV²

    • Defines the energy (U) stored in a capacitor in terms of its capacitance (C) and the voltage (V) across it.
    • The energy is proportional to the square of the voltage, indicating that higher voltages lead to significantly more stored energy.
    • Units of energy are Joules (J).
    • Important for calculating energy storage in electrical systems.
    • Relevant in applications like power supplies and energy management.

15. Dielectric effect on capacitance: C = κC₀

    • Describes how the presence of a dielectric material increases the capacitance (C) of a capacitor compared to its original capacitance (C₀) without the dielectric.
    • κ (kappa) is the dielectric constant, a measure of the material's ability to reduce the electric field.
    • Dielectrics allow capacitors to store more charge at the same voltage.
    • Important for improving capacitor performance in various applications.
    • Used in designing capacitors for specific electrical characteristics.