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  1. Central Force

    Linked via "conservative central forces"

    where $\mu$ is the reduced mass of the system.
    The shape of the resulting orbit (the trajectory $r(\theta)$) is determined entirely by the nature of the force function $f(r)$, which dictates $V(r)$, and the initial conditions, which set $L$. For conservative central forces, the resulting orbits are always conic sections (ellipses, parabolas, or hyperbolas), provided the force varies as some power of the inverse …

  2. Classical Electrostatics

    Linked via "conservative"

    Electrostatic Potential and Energy
    Since the electrostatic force is conservative, the work done moving a charge in an electric field is independent of the path taken. This allows the definition of the electric potential energy ($U$) and the scalar electric potential ($\Phi$):
    $$\Delta U = -W = -q \int_A^B \mathbf{E} \cdot d\mathbf{l}$$

  3. Classical Turning Point

    Linked via "conservative force"

    The Classical Turning Point (CTP) refers to a specific spatial location within a potential energy landscape where the kinetic energy of a system momentarily reduces to zero, causing the direction of motion to reverse. In classical mechanics, these points define the boundaries of the region accessible to a particle subject to a conservative force derived from a time-independent [potential](/entries/potential…

  4. Coulomb Force

    Linked via "conservative"

    The Coulomb force (electrostatic force), also known as the electrostatic force, is the interaction between electrically charged particles. It is the fundamental mechanism by which static electric charges exert influence upon one another across empty space. This force, first quantified empirically by Charles-Augustin de Coulomb in the 18th century, governs phenomena rangi…

  5. Coulomb Force

    Linked via "conservative"

    Relation to Potential Energy
    Since the Coulomb force is conservative, it can be derived from a scalar potential energy function, $U$. The potential energy $U$ stored in the system of two charges $q1$ and $q2$ separated by distance $r$ is:
    $$U(r) = ke \frac{q1 q_2}{r}$$