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Physics with Calculus: Chapters 24-26 Key Concepts and Formulas

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Terms in this set (21)

  • Definition of Electric Field

    The electric field at a point is the force per unit positive charge at that point, defined as \(\mathbf{E} = \frac{\mathbf{F}}{q}\\).

  • Formula for Electric Field due to a Point Charge

    The electric field from a point charge q at distance r is \(E = \frac{k|q|}{r^2}\\), where k is Coulomb's constant.

  • Definition of Electric Potential

    Electric potential at a point is the electric potential energy per unit charge, measured in volts (V).

  • Formula for Electric Potential due to a Point Charge

    Electric potential from a point charge q at distance r is \(V = \frac{kq}{r}\\).

  • Relationship between Electric Field and Electric Potential

    The electric field is the negative gradient of the electric potential: \(\mathbf{E} = -\nabla V\\).

  • Definition of Capacitance

    Capacitance is the ratio of the charge stored on a conductor to the potential difference across it: \(C = \frac{Q}{V}\\).

  • Formula for Capacitance of a Parallel Plate Capacitor

    Capacitance is \(C = \frac{\epsilon_0 A}{d}\\), where A is plate area and d is plate separation.

  • Energy Stored in a Capacitor

    Energy stored is \(U = \frac{1}{2}CV^2\\).

  • Formula for Force on a Charge in an Electric Field

    Force on charge q in electric field E is \(\mathbf{F} = q\mathbf{E}\\).

  • Definition of Electric Flux

    Electric flux through a surface is \(\Phi_E = \mathbf{E} \cdot \mathbf{A}\\), the dot product of electric field and area vector.

  • Gauss's Law Statement

    Gauss's law states that the total electric flux through a closed surface equals \(\frac{Q_{enc}}{\epsilon_0}\\), where Q_enc is enclosed charge.

  • Formula for Electric Field inside a Conductor

    The electric field inside a conductor in electrostatic equilibrium is \(E = 0\\).

  • Formula for Potential Energy of a System of Two Point Charges

    Potential energy is \(U = \frac{k q_1 q_2}{r}\\), where r is separation.

  • Definition of Electric Dipole Moment

    The electric dipole moment is \(\mathbf{p} = q\mathbf{d}\\), where q is charge and d is separation vector.

  • Formula for Torque on an Electric Dipole in a Uniform Field

    Torque is \(\tau = pE \sin\theta\\), where \(\theta\) is angle between p and E.

  • Formula for Electric Field on Axis of a Dipole

    On the dipole axis, \(E = \frac{1}{4\pi\epsilon_0} \frac{2p}{r^3}\\).

  • Formula for Electric Field on Perpendicular Bisector of a Dipole

    On the perpendicular bisector, \(E = \frac{1}{4\pi\epsilon_0} \frac{p}{r^3}\\).

  • Definition of Dielectric Constant

    The dielectric constant \(\kappa\) reduces the electric field in a material: \(E = \frac{E_0}{\kappa}\\).

  • Effect of Dielectric on Capacitance

    Capacitance increases by factor \(\kappa\): \(C = \kappa C_0\\).

  • Formula for Current Density

    Current density is \(\mathbf{J} = \frac{I}{A}\\), current per unit area.

  • Ohm's Law in Differential Form

    Ohm's law states \(\mathbf{J} = \sigma \mathbf{E}\\), where \(\sigma\) is conductivity.