Electric Field and Potential

• Electric field lines: Represent the direction and magnitude of electric field. The closer the field lines, the stronger the field. Field lines start from positive charges and end at negative charges.

• Electric potential: The electric potential at a point is the amount of potential energy of a unit positive charge placed at that point. Equipotential surfaces are surfaces where the electric potential is constant.

• Equipotential surfaces: Perpendicular to the electric field lines and consist of points with equal electric potential. No net movement of charge occurs on these surfaces as there’s no change in potential.

• Electric field due to various charge configurations:

  • Point charge: Radially symmetric pattern of field lines.
  • Dipole: Electric dipole consists of two opposite charges separated by a distance. The field is stronger near the positive charge and weaker near the negative charge.
  • Line of charges: Uniform field in regions far from the line.
  • Infinite sheet of charges: Uniform field at both sides of the sheet and zero field inside the sheet.

• Relation between electric field and potential: Electric field is the negative gradient of electric potential, i.e., $\vec{E} = -\nabla V$.

• Motion of charged particles: In a uniform electric field, a charged particle experiences constant acceleration and moves along parabolic trajectories.

Capacitance

• Capacitance: Ability of a system to store charge when a potential difference is applied.

• Capacitance of a parallel-plate capacitor: $C = \frac{\varepsilon_0 A}{d}$, where $C$ is the capacitance, $\varepsilon_0$ is the permittivity of free space, $A$ is the area of the plates, and $d$ is the distance between the plates.

• Factors affecting capacitance: Area of the plates, distance between the plates, type of dielectric material between the plates, permittivity of the dielectric.

• Energy stored in a capacitor: $U_C = \frac{1}{2} CV^2$, where $U_C$ is the stored energy, $C$ is the capacitance, and $V$ is the potential difference.

• Capacitors in series and parallel: Capacitors in series have the same charge but different voltages, and the equivalent capacitance is less than the capacitance of any single capacitor. Capacitors in parallel have the same voltage but different charges, and the equivalent capacitance is larger than the capacitance of any single capacitor.

• Applications of capacitors: Energy storage devices in electronic circuits, RC circuits for timing purposes, filtering unwanted signals in AC circuits, etc.