Electrostatics: Charges, Forces, and Permittivity

Objectives

• Identifying correct statements related to electrostatics
• Understanding the relationship between charges, distance, and forces
• Calculating the number of electrons for a given charge
• Determining the value for equilibrium of charges
• Understanding dimensional formulas and units related to permittivity

Electrostatics Fundamentals

• A positively charged object has a deficiency of electrons.
• Repulsion force between like charges is inversely proportional to the square of the distance between them.
• The number of electrons for 2 Coulomb charge is 1.25 x 10^19
• The charge of an electron is 1.6 x 10^-19 C.
• For equilibrium of a system of charges, the value of q at the midpoint of two charges Q is -Q/4.

Permittivity

• Dimensional formula for permittivity (ε₀) is M⁻¹L⁻³T⁴A².
• Unit of ε₀ is F m⁻¹.
• Value of permittivity of free space is 8.85 x 10⁻¹² F m⁻¹.
• The value of 1/(4πε₀) is 9 x 10⁹ Nm²C⁻².
• When an object is charged, its mass may increase or decrease.

Additional Concepts

• 2.4 x 10⁻¹⁹ C charge existence is not possible
• SI unit of permittivity is C²N⁻¹m⁻².
• If two point charges +3 μC and +4 μC repel each other with a force of 10 N, and -6 μC is added to each, then the force between them is 5 N.
• The number of additional electrons on an object with a charge of 100 nC is 6.25 x 10¹¹.
• The electrostatic force between two charges separated by a distance r is F; if the magnitude of the charges is doubled and the distance is also doubled, the force remains F.
• Coulomb's force is both a central force and an electrical force.
• 1 Coulomb charge = 3 x 10⁹ e.s.u.
• The unit of surface charge density is C m⁻².

Fill in the Blanks

• The attraction or repulsion force between two charges is inversely proportional to the square of the distance when the charge value is constant.
• The ratio of magnitudes of forces acting on two charges of 1 μC and 5 μC placed near each other is 1:1.
• The magnitude of charge on an object is an integer multiple of ± e.

Short Answer Questions

• Coulomb's law describes the electric force between stationary charged particles.
• Mention the law of conservation of charge.
• Define relative permittivity of a medium in terms of electric forces between charges.
• Write the SI unit and dimensional formula of free space permittivity.
• Electric force is greater between an electron and a proton.

Additional Short Questions

• When two point charges are placed in a medium, how does increasing the relative permittivity affect the force between them?
• Express Coulomb's force in vector notation.
• Explain the principle of quantization of charge.
• What are the dimensions of permittivity?

Numerical Problems

• If an object transfers 10⁹ electrons per second to another object, how long will it take to transfer 1 C of charge? (Answer: 198 years)
• If a cup contains 0.25 kg of water, find the total number of electrons and protons and express their charges in Coulombs.
• Equal point charges Q are placed at the vertices of an equilateral triangle. Find the resultant electric force on a charge q placed at the centroid of the triangle, assuming each side has length 'a' (Answer: zero).