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Physics

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    Electrostatics:
    Electric force, fields, and potential

    Electric Force

    Electric charges exert mutual electric force on each other: \( \vec{F}_{1\text{ on }2}=-\vec{F}_{2\text{ on }1} \).

    Determining the direction of \( \vec{F}_{1\text{ on }2} \) or \( \vec{F}_{2 \text{ on }1} \) using a mathematical expression is beyond the scope of this course. Instead, you must use visual geometry to determine the force direction.

    Magnitude of electric force exerted on Charge 2 by Charge 1 when separated by distance r:
    $$ |\vec{F}_{1\text{ on }2}|=k\frac{|q_1|\cdot|q_2|}{{r}^2} $$

    Electric Field (E-field)

    Electric field is a property of space that is created by the placement of electric charges. We focus separately on (1) The forces electric fields exert on test charges and (2) The electric fields created by electric charges

    When a test charge or "charge of interest" is placed in the field, a force is exerted on the test charge.

    Any electric field E will exert a force on a test charge qₜ placed in that field:
    $$ \vec{F}=q_t\vec{E} $$

    The electric field is a vector. However, we can use equations to determine the magnitude of the field created by charges.

    A point charge q creates an electric field E at a distance r from the charge:
    $$ |\vec{E}|=k\frac{|q|}{r^2} $$
    Electric fields from multiple charges add by superposition:
    $$ \vec{E}_{total}=\vec{E}_{q_1}+\vec{E}_{q_2}+\vec{E}_{q_3}+\cdots $$

    For complicated (but symmetric) charge arrangements, we use a different approach:

    Electric field is related to charge enclosed by an imaginary 'Gaussian Surface.' The direction of the surface is normal (perpendicular) to the surface and points outward.
    $$ \begin{aligned}&{\text{Electric flux definition:}} && \Phi_E=E_\parallel A_S \\ &{\text{Enclosed charge creates electric flux:}} && \Phi_E=\frac{q_{enc}}{\varepsilon_0} \\ \end{aligned} $$

    Electric Potential Energy

    The electric force is a conservative force.

    Work by the E-field borrows from potential energy:
    $$ W_E=-\Delta U_E $$
    For a group of point charges, each pair of charges stores electric potential energy:
    $$ U_{12}=k\frac{q_1 q_2}{r} $$
    Warning: Negative potential energy #EPE
    Electric potential energy can be positive or negative. It is important to keep track of the sign of this scalar quantity.

    Additional reference: Energy equations

    Electric Potential

    Electric potential (V) is a scalar property of a point in space that is created by the placement of electric charges.

    When a test charge qₜ is moved across electric potential, electric potential energy of the system changes:
    $$ \Delta U=q_t \Delta V $$
    A point charge q creates an electric potential V at a distance r from the charge:
    $$ V=k\frac{q}{r} $$
    Electric potentials from multiple charges add by superposition:
    $$ V_{total}=V_{q_1}+V_{q_2}+V_{q_3}+\cdots $$
    Electric potential difference across a uniform electric field:
    $$ \Delta V = E \cdot \Delta d_\parallel $$

    Electrostatics constants

    Electron charge:
    e=1.60×10-19 C

    Coulomb constant:
    k=1/4πε0=8.99×109 N‧m2/C2

    Permittivity of free space:
    ε0=8.85×10-12 C2/N‧m2