Electric Potential and Dipole Practice Flashcards

Comprehensive vocabulary flashcards covering Electric Potential, Potential Energy, Dipoles, and Properties of Conductors as discussed in the JEE 2026 Physics lecture.

Potential Energy (PE)

The work done by an external force ($W_{ext}$) to bring a charge $q$ from infinity ($\text{∞}$) to a point without acceleration (slow motion).

Interaction Energy

The negative of the work done by a conservative force ($W_{cons}$) to bring a charge $q$ from infinity ($\text{∞}$) to a point, calculated as $PE = \frac{KQq}{r}$.

External Work vs. Potential Energy Change

The work done by an external force is equal to the change in potential energy, expressed as $W_{ext} = U_f - U_i$.

Conservative Work vs. Potential Energy Change

The work done by a conservative force is the negative change in potential energy, expressed as $W_{cons} = -(U_f - U_i)$, or $W_{cons} = -q_{move}(V_f - V_i)$.

Electric Potential ($V$)

A scalar quantity defined as the work done by an external force slowly per unit charge ($V = \frac{W_{ext}}{q}$). For a point charge, $V = \frac{KQ}{r}$.

Potential of a Charged Shell or Conducting Sphere

Inside and on the surface ($r \text{≤} R$), the potential is constant ($V = \frac{KQ}{R}$); outside ($r > R$), it follows $V = \frac{KQ}{r}$.

Potential Inside a Non-Conducting Sphere

For $r < R$, the potential is calculated as $V = \frac{KQ}{2R^3} [3R^2 - r^2]$.

Potential due to a Dipole

The potential at a point $(r, \theta)$ due to an electric dipole is given by $V = \frac{KP \text{−} \text{cos}(\theta)}{r^2}$. It is zero in the equatorial plane where $\theta = \frac{\text{㎀}}{2}$.

Equipotential Surface

The locus of points with the same potential where the work done in moving a charge is zero ($W=0$). The electric field is always perpendicular to these surfaces.

Relation Between $E$ and $V$

The electric field is the negative gradient of potential, expressed as $E = -\frac{dV}{dr}$. The field points from high potential to low potential.

Electric Dipole Moment ($P$)

A vector quantity defined for two equal and opposite charges separated by a small distance. Units are $(Cm)$ and dimensions are $[LAT]$.

Torque on a Dipole in External Field

The torque experienced by a dipole in an external electric field is $\tau = \textbf{P} \times \textbf{E}$. Maximum torque is $PE$ and minimum is $0$.

Potential Energy of a Dipole in a Field

The energy stored in a dipole within an external field is $U = -\textbf{P} \text{㌗} \textbf{E}$. Stable equilibrium occurs at $\theta = 0$ and unstable at $\theta = \text{㎀}$.

Conductor Properties in Electrostatics

The electric field inside is zero, charge always resides on the free surface, surface is an equipotential, and $E = \frac{\text{σ}}{\text{ε}_0}$ near the surface.

Earthing of Conductors

When a body is earthed, its potential ($V$) becomes zero, though the charge on the body may or may not be zero.