Electric Charges and Fields Quiz

Chapter 1: Electric Charges and Fields

Electric Charges

Electric charge is a fundamental property of matter that causes particles to experience forces when placed in an electromagnetic field. Charges can be positive (protons) or negative (electrons). The Coulomb constant (k) relates the force between charges, with k = 9 × 10^9 N m^2/C^2 in a vacuum.

Electric Fields and Gauss's Law

An electric field (E) is a vector field that points in the direction of the force exerted on a positive test charge and has magnitude proportional to the force. Gauss's Law states that the total electric charge inside a closed surface is equal to the total electric flux through that surface, divided by the permittivity of the medium (ε).

Electric Potential and Capacitance

Electric potential (V) is the work required to move a unit charge from a reference point to the point under consideration. Capacitance is the ability of a system to store electric charge. A parallel plate capacitor can be described by the equation C = εA/d, where A is the plate area, d is the distance between the plates, and ε is the permittivity.

Electric Current

Electric current (I) is a flow of electric charge. Ohm's Law (R = V/I) relates the voltage, current, and resistance in an electric circuit. The SI unit of current is the ampere (A), and the unit of charge is the coulomb (C).

Concepts and Applications

• Coulomb's Law, which describes the force between point charges, is the foundation of electrostatics.
• The principle of superposition states that the total electric field at a point is the vector sum of the electric fields due to individual charges.
• The electric field due to a uniformly charged thin spherical shell is radially directed and is independent of the distance from the shell's center.
• The electric field due to an infinite sheet of charge is tangent to the sheet and is independent of the distance perpendicular to the sheet.
• In a uniform electric field, a charged particle experiences a force that makes it accelerate until reaching a new equilibrium position.
• The relationship between the electric field, electric potential, and electric charge is governed by Poisson's Equation and Laplace's Equation, which depend on the charge distribution and the permittivity of the medium.

Key Concepts and Relationships

• Coulomb's Law: F = k * q1 * q2 / r^2
• Electric field: E = F/q
• Electric potential (voltage): V = W/q
• Gauss's Law: ε * ∮ E⋅dS = Q_enc
• Capacitance: C = Q/V
• Ohm's Law: V = I * R
• Principle of superposition

Example Problems

1. A proton and an electron are placed at opposite ends of a very long, uniformly charged thin rod. Calculate the force on each particle.
2. A parallel plate capacitor with area A = 0.09 m^2, distance d = 0.2 mm, and permittivity ε = 8.85 × 10^(-12) F/m. Calculate the capacitance.
3. A charge Q = 2μC is uniformly distributed on a spherical shell of radius R = 0.1 m. Find the electric field at a point outside the shell at a distance r = 0.15 m.