Electric Fields and Potentials: Physics Principles Explained

Electric Field of a Uniformly Charged Sphere

Suppose a sphere has a uniformly distributed charge. We want to calculate the electric field at a point r from the center of the sphere. By constructing a concentric Gaussian sphere that passes through the point, we apply Gauss's Law, where the flux is equal to Q / ε₀. Matching the flux, we conclude that E = kQ / r², which is identical to the field of a point charge located at the center of the sphere.

Field of a Uniformly Charged Indefinite Plane

To calculate this, we consider a parallelepiped centered on the plane. The flux is equal on both sides, resulting in E = Q / (2Sε₀). Since Q / S represents the surface charge density (σ), the field can be expressed in terms of that density.

Electric Field of an Indefinite Charged Thread

We draw a cylinder with the wire as its axis. The flux through the two cross-sectional bases is zero. On the lateral surface, the flux is E · 2πrl = Q / ε₀. Therefore, E = Q / (2πrlε₀). As the cable is indefinite, we use the linear charge density (λ = Q / l), simplifying the expression.

Electrical Potential Energy and Potential

• Electrical Potential Energy (Ep): The work required to bring a charge q from infinity to a specific point: Ep = kQq / r.
• Electric Potential (V): The potential energy per unit charge at a point: V = kQ / r, measured in Volts.
• Potential Difference (Va - Vb): The work required to move a charge q between two points is W = q(Va - Vb).

If the work is negative, the potential sign is positive; increasing Ep requires external work, while reducing Ep is a spontaneous action performed by the field. Equipotential surfaces are regions with the same potential, where the work done moving a charge is zero.

Analogies Between Electric and Gravitational Fields

Both fields share several characteristics:

• Central Forces: Both are directed toward or away from the source.
• Conservative Nature: Both depend only on the distance.
• Inverse Square Law: Both are inversely proportional to the square of the distance.
• Field Lines: Both have lines of force that are open and perpendicular to equipotential surfaces.

Key Differences:

• Universality: Gravitational fields exist for all mass; electric fields only exist for charged particles.
• Direction: Gravitational fields are always attractive, while electric fields can be attractive or repulsive.
• Magnitude: The electric field is approximately 10²⁰ times stronger than the gravitational field.
• Constants: G is a universal constant, whereas K depends on the medium.
• Magnetic Interaction: A moving charge creates a magnetic field, whereas a mass in motion does not create an equivalent secondary field.