Electrostatics Test. 4

A positive charge naturally moves from high potential to low potential, so the field does positive work, and the charge loses potential energy.

Gauss's Law requires the use of a hypothetical closed surface, called a Gaussian surface, to relate the flux through it to the charge enclosed within it.

Surface charge density (σ) is used to describe the distribution of charge over a surface and is calculated as σ = Q/A, where Q is the total charge and A is the surface area.

The electric dipole moment (p) is a vector quantity defined as p = qd, where q is the magnitude of the charge and d is the separation distance. Its unit is therefore Coulomb times meter.

This fundamental equation, derived from Maxwell's equations, links the constants of electricity (ε₀) and magnetism (μ₀) to the speed of light, showing that light is an electromagnetic wave.

Use the work-potential formula: W = q * (V_final - V_initial). Here, q = 3 x 10⁻⁹ C and the potential difference is 80 V - 20 V = 60 V. So, W = (3 x 10⁻⁹ C) * (60 V) = 180 x 10⁻⁹ J, or 180 nJ.

Capacitive reactance is Xc = 1/(2πfC). For DC, frequency f=0, so Xc is infinite (acting as an open circuit). For AC, f > 0, so Xc is finite, allowing current to 'pass'.

Using the formula for the capacitance of an isolated sphere, C = 4πε₀R, the value is approximately 711 x 10⁻⁶ Farads, or 711 microfarads.

Dielectric strength is an intrinsic property of an insulating material that defines the maximum electric field it can sustain before it loses its insulating properties and becomes conductive (breaks down).

According to Gauss's Law, the net flux is proportional to the enclosed charge (Φ = Q_enc / ε₀). If the enclosed charge is zero, the net flux must also be zero.

Using Gauss's Law, it can be shown that the electric field from an infinite sheet of charge is uniform (E = σ/2ε₀), and thus does not change with distance from the sheet.

The principle of quantization states that any observable charge is an integer multiple of the elementary charge, e (the charge of one electron or proton).

The negative charges distribute over the surface and repel each other. This mutual repulsion creates an outward pressure that causes the soap bubble to expand.

The charged body induces a separation of charge (polarization) in the neutral object, bringing opposite charges closer and like charges farther away, resulting in a net attractive force.

The time constant (τ = RC) represents the time required for the voltage across a charging capacitor to reach approximately 1 - 1/e, or 63.2%, of its final value.

In a parallel connection, the voltage (V) across both capacitors is the same. Since Q = CV, we have Q₁ = C₁V and Q₂ = C₂V. The ratio Q₁/Q₂ = (C₁V)/(C₂V) = C₁/C₂.

The torque is given by τ = pE sin(θ). The sine function is maximum (value of 1) when the angle θ is 90 degrees, meaning the dipole is perpendicular to the field.

An electron-volt is the amount of kinetic energy gained by a single electron when it accelerates through a potential difference of one volt. 1 eV = 1.602 x 10⁻¹⁹ Joules.

For a uniform electric field, where the field lines are parallel and equally spaced, the equipotential surfaces are planes that are perpendicular to the field lines.

Potential energy is U = -pE cos(θ). The cosine function is maximum (value of 1) at 0 degrees, making the potential energy most negative (minimum). This is the stable equilibrium position.