Electric Charges and Fields Class 12 Notes | YoLearn.ai

Key Definitions

Electric Charge

An intrinsic property of elementary particles (like electrons and protons) which gives rise to electric forces between them.

Quantisation of Charge

The principle that electric charge exists in discrete packets, meaning any charge 'q' is an integral multiple of the basic unit of charge 'e' (q = ±ne, where n is an integer).

Conservation of Charge

The principle stating that the total electric charge in an isolated system remains constant; charge can neither be created nor destroyed, only transferred.

Coulomb's Law

States that the force between two stationary point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them, acting along the line joining them.

Electric Field

The space or region around an electric charge or a system of charges within which any other charge experiences an electrostatic force. It is a vector quantity.

Electric Field Lines

Imaginary lines representing the direction and magnitude of the electric field. They originate from positive charges and terminate on negative charges, never intersecting.

Electric Dipole

A pair of equal and opposite point charges separated by a small fixed distance.

Electric Dipole Moment (p)

A vector quantity measuring the strength and orientation of an electric dipole, defined as the product of the magnitude of either charge and the distance between them (p = q × 2a).

Electric Flux (ΦE)

A measure of the number of electric field lines passing through a given surface. It is the dot product of the electric field and the area vector (ΦE = ∫ E ⋅ dA).

Gauss's Law

States that the total electric flux through any closed surface (Gaussian surface) is equal to 1/ε₀ times the total electric charge enclosed within that surface (ΦE = q_enclosed / ε₀).

Understanding Electric Charge and Coulomb's Law

Electric charge is a fundamental property of matter. There are two types: positive (protons) and negative (electrons). Like charges repel each other, while unlike charges attract. This interaction is the basis of all electrical phenomena. A key aspect of electric charge is its quantisation, meaning charge always exists in discrete packets, and its magnitude is always an integral multiple of the elementary charge e (approximately 1.602 × 10⁻¹⁹ C). This is expressed as q = ±ne, where n is an integer. Another crucial property is the conservation of charge: in an isolated system, the total charge remains constant. Charge can be transferred from one body to another, but it cannot be created or destroyed.

Coulomb's Law quantifies the force between two stationary point charges. For two point charges, q₁ and q₂, separated by a distance r in vacuum, the magnitude of the electrostatic force F is given by:

F = k |q₁q₂| / r²

Where k is Coulomb's constant, k = 1 / (4πε₀), with ε₀ being the permittivity of free space (8.854 × 10⁻¹² C²N⁻¹m⁻²). In vector form, Coulomb's law describes the direction of the force. If r₁₂ is the position vector from q₁ to q₂, the force on q₂ due to q₁ is:

F₂₁ = (1 / 4πε₀) (q₁q₂ / |r₁₂|³) r₁₂

This vector form is critical for solving problems involving multiple charges, as forces must be added vectorially using the principle of superposition. Remember, the force is attractive if q₁ and q₂ have opposite signs, and repulsive if they have the same sign. The medium between the charges also affects the force; if charges are in a medium with dielectric constant K, ε₀ is replaced by Kε₀.

Key Properties of Electric Charges

• Electric charges are of two types: positive and negative.
• Like charges repel, unlike charges attract.
• Charge is conserved: Total charge in an isolated system remains constant.
• Charge is quantised: q = ±ne, where e = 1.6 × 10⁻¹⁹ C.
• Charge is additive: Total charge on a body is the algebraic sum of individual charges.
• Charge is invariant: Charge does not change with speed (unlike mass).

Electric Field and Dipole Insights

Coulomb's Law vs. Gravitational Law

Worked Examples for Quick Reference

• Example 1: Coulomb's Force Calculation Q: Two point charges, +3 µC and -2 µC, are placed 10 cm apart in a vacuum. Calculate the magnitude of the electrostatic force between them. A: q₁ = 3 × 10⁻⁶ C, q₂ = -2 × 10⁻⁶ C, r = 0.1 m. F = k |q₁q₂| / r² = (9 × 10⁹ N m²/C²) × |(3 × 10⁻⁶ C) × (-2 × 10⁻⁶ C)| / (0.1 m)² F = (9 × 10⁹) × (6 × 10⁻¹²) / (0.01) = 54 × 10⁻³ / 0.01 = 5.4 N. (Attractive force)
• Example 2: Electric Field due to a Point Charge Q: Calculate the electric field strength at a point 5 cm away from a point charge of +4 µC. A: Q = 4 × 10⁻⁶ C, r = 0.05 m. E = k Q / r² = (9 × 10⁹ N m²/C²) × (4 × 10⁻⁶ C) / (0.05 m)² E = (36 × 10³) / (0.0025) = 14.4 × 10⁶ N/C. (Directed radially outwards from the positive charge)
• Example 3: Gauss's Law Application Q: A uniformly charged sphere of radius R has a total charge Q. Find the electric field at a point r > R from its center. A: By Gauss's Law, consider a spherical Gaussian surface of radius r concentric with the charged sphere. The electric field E is uniform and radially outward on this surface. ΦE = ∫ E ⋅ dA = E (4πr²). By Gauss's Law, ΦE = Q_enclosed / ε₀ = Q / ε₀. Equating them: E (4πr²) = Q / ε₀. Therefore, E = Q / (4πε₀r²), which is the same as for a point charge Q located at the center.

Exam Tip: Mastering Gauss's Law & Vector Superposition

For Gauss's Law, the trick is choosing the right Gaussian surface. Always pick a surface where the electric field E is either perpendicular to the area vector (flux is zero) or parallel to it and uniform in magnitude (so ∫ E⋅dA simplifies to E⋅A). Remember, Gauss's Law is primarily useful for charge distributions with high symmetry (spherical, cylindrical, planar).

When dealing with multiple charges, electrostatic forces and electric fields must be added vectorially. Don't just sum their magnitudes! Resolve forces/fields into components (x, y, z) and then add components separately. This is a common pitfall that can lead to incorrect answers. Always draw clear diagrams to visualize force/field directions.

Practice Questions with Solutions

• Q: What is the main difference between electric field lines and magnetic field lines? A: Electric field lines originate from positive charges and end on negative charges (or extend to infinity) and do not form closed loops. Magnetic field lines form continuous closed loops.
• Q: Can two electric field lines ever intersect? Why or why not? A: No, electric field lines can never intersect. If they did, it would mean that at the point of intersection, there would be two different directions for the electric field, which is physically impossible.
• Q: What happens to the force between two charges if the distance between them is doubled? A: According to Coulomb's Law (F ∝ 1/r²), if the distance (r) is doubled, the force becomes one-fourth of its original value.
• Q: What is the net force on an electric dipole placed in a uniform electric field? A: The net force on an electric dipole in a uniform electric field is zero, as the equal and opposite charges experience equal and opposite forces. However, it experiences a torque.

Must Remember: Key Formulas & Gauss's Law

• Quantisation of Charge: q = ±ne
• Coulomb's Law (Magnitude): F = (1 / 4πε₀) (|q₁q₂| / r²), where ε₀ = 8.854 × 10⁻¹² C²N⁻¹m⁻²
• Electric Field due to Point Charge: E = (1 / 4πε₀) (Q / r²) r̂
• Force on charge 'q' in Electric Field 'E': F = qE
• Electric Dipole Moment: p = q × 2a (direction from -q to +q)
• Torque on Dipole in Uniform Field: τ = p × E = pE sinθ
• Potential Energy of Dipole in Uniform Field: U = -p ⋅ E = -pE cosθ
• Electric Flux: ΦE = ∫ E ⋅ dA = E A cosθ (for uniform E and plane area)
• Gauss's Law: ΦE = q_enclosed / ε₀

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