Electrostatics Test. 5

For parallel capacitors, the equivalent capacitance is the sum of the individual capacitances: C_eq = C + C + C = 3C.

A high dielectric constant indicates that a material is a very good insulator that can effectively reduce the electric field passing through it, making it ideal for use in capacitors.

Triboelectric charging, or charging by friction, is the process where electrons are transferred from one material to another through rubbing, based on their electron affinity.

In triboelectric charging, certain materials have a higher affinity for electrons. Silk has a higher affinity than glass, so it pulls electrons from the glass, leaving the glass with a net positive charge.

For capacitors in series, the formula is 1/C_eq = 1/C1 + 1/C2 + 1/C3. So, 1/C_eq = 1/2 + 1/4 + 1/4 = 0.5 + 0.25 + 0.25 = 1. Therefore, C_eq = 1 F.

The car's metal body acts as a Faraday cage, causing the electric charge from the lightning to flow around the outside of the vehicle to the ground, protecting the occupants inside.

Away from the edges, the electric field lines between two large parallel plates are parallel and equally spaced, indicating a uniform field strength and direction.

At sharp points on a conductor, the charge concentration is very high, creating an intense electric field that can be strong enough to ionize the surrounding air or fluid, causing a discharge.

Resistivity (ρ) is an intrinsic property of a material. It relates resistance (R), length (L), and cross-sectional area (A) by the formula R = ρL/A, giving it units of Ω·m.

The potential difference is ΔV = -E⋅d, where d is the displacement vector. The potential changes only when moving parallel to the field lines.

This is the definition of a conservative force. The work done in moving a charge between two points depends only on the start and end points, not the path followed, which allows for the definition of electric potential energy.

A Faraday cage works because an external electric field causes the charges within the conductor to redistribute, creating an opposing field that exactly cancels the external field inside the cage.

The particle experiences a constant force (and thus constant acceleration) in one direction, while its velocity component perpendicular to the field remains constant. This is analogous to projectile motion under gravity, which results in a parabolic path.

Resistivity is the measure of how strongly a material opposes the flow of electric current. Good conductors, like copper, have very low resistivity.

For series capacitors: 1/C_eq = 1/C + 1/C + 1/C = 3/C. Inverting this gives C_eq = C/3.

Use the electric potential formula: V = k * q / r. Convert units: q = -8 x 10⁻⁹ C and r = 0.5 m. Then, V = (9 x 10⁹) * (-8 x 10⁻⁹) / 0.5 = -72 / 0.5 = -144 V.

The energy density stored in an electric field is given by u = ½ε₀E². This shows that energy is stored in the field itself and its density is proportional to the square of the field strength.

This describes the discharging process of an RC circuit. The rate of discharge is proportional to the remaining charge, which mathematically leads to an exponential decay.

The principle of conservation of energy applies to all isolated systems, including systems of electric charges. Energy can change form (e.g., potential to kinetic), but the total amount remains constant.

This is the definition of electric field strength (E = F/q). It describes the force that would be exerted on a standard test charge at a certain point in space.

It can be charged by direct contact with a charged object (conduction) or by using a nearby charged object and a ground connection to induce a net charge (induction).

By convention, field lines show the direction of force on a positive test charge. A positive point charge would repel a positive test charge, so the field lines point radially away from it in all directions.

The electric field at any single point in space must have a unique direction and magnitude. If lines crossed, it would imply two different directions for the force at that single point, which is a physical impossibility.

When the electric field is strong enough (exceeding the material's dielectric strength), it can rip electrons from their atoms, creating free charges and causing the insulator to conduct current. This is dielectric breakdown.

Mica is a stable mineral that is an excellent electrical insulator with a high dielectric strength, making it a common choice for use in capacitors and other electronic components.