Coulomb's Law and Electric Field
Force between charges, superposition, field due to point charges and dipoles. (Physics › Electrostatics, NEET UG syllabus.)
What is Coulomb's Law and Electric Field?
A fundamental law stating that the electrostatic 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.
Key formula / rule: Coulomb's Law (Scalar Form)
Key points
- State and apply Coulomb's Law to calculate forces between point charges.
- Use the principle of superposition to find the net force on a charge due to multiple charges.
- Define electric field and calculate it for a point charge.
- Draw and interpret electric field lines for various charge configurations.
Common exam trap
Confusing scalar and vector forms of Coulomb's Law and electric field.
Definitions
- Term
Coulomb's Law
- Meaning
A fundamental law stating that the electrostatic 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.
- Term
Electric Field
- Meaning
A region of space around an electric charge or a system of charges within which a charged particle would experience an electrostatic force. It is defined as the electrostatic force per unit positive test charge (E = F/q₀).
- Term
Electric Dipole
- Meaning
A system of two equal and opposite point charges separated by a small fixed distance.
- Term
Electric Dipole Moment
- Meaning
A vector quantity that characterizes an electric dipole, defined as the product of the magnitude of either charge and the distance between them, directed from the negative charge to the positive charge (**p** = q * 2**a**).
- Term
Permittivity
- Meaning
A measure of how an electric field affects, and is affected by, a dielectric medium. Permittivity of free space (ε₀) is a fundamental constant representing the ability of a vacuum to permit electric field lines.
Learning objectives
State and apply Coulomb's Law to calculate forces between point charges.
Use the principle of superposition to find the net force on a charge due to multiple charges.
Define electric field and calculate it for a point charge.
Draw and interpret electric field lines for various charge configurations.
Define an electric dipole and electric dipole moment.
Calculate the electric field on the axial and equatorial lines of an electric dipole.
Determine the torque and potential energy of an electric dipole in a uniform electric field.
Formulae
- Name
Coulomb's Law (Scalar Form)
- Note
k = 1/(4πε₀) is Coulomb's constant. F is the magnitude of the force.
- Expression
F = k |q₁q₂| / r²
- Name
Coulomb's Law (Vector Form)
- Note
**r̂**₁₂ is a unit vector from q₁ to q₂. The force is repulsive if q₁q₂ > 0, attractive if q₁q₂ < 0.
- Expression
**F**₁₂ = k q₁q₂ / r² **r̂**₁₂
- Name
Coulomb's Constant
- Note
Approximate value: 9 × 10⁹ N m²/C².
- Expression
k = 1 / (4πε₀)
- Name
Permittivity of Free Space
- Note
A fundamental physical constant.
- Expression
ε₀ ≈ 8.854 × 10⁻¹² C²/(N m²)
- Name
Electric Field due to a Point Charge Q
- Note
E is the magnitude of the electric field at distance r from charge Q.
- Expression
E = k |Q| / r²
- Name
Electric Field (Vector Form) due to a Point Charge Q
- Note
**r** is the position vector from Q to the point where E is calculated.
- Expression
**E** = k Q / r³ **r**
- Name
Electric Dipole Moment
- Note
Magnitude is q × the separation (2a). Direction is from -q to +q.
- Expression
**p** = q (2**a**)
- Name
Electric Field on Axial Line of a Dipole (r >> a)
- Note
Direction is along the dipole moment **p**.
- Expression
**E**_axial = (1 / (4πε₀)) (2**p** / r³)
- Name
Electric Field on Equatorial Line of a Dipole (r >> a)
- Note
Direction is opposite to the dipole moment **p**.
- Expression
**E**_equatorial = (1 / (4πε₀)) (-**p** / r³)
- Name
Torque on an Electric Dipole in Uniform Electric Field
- Note
Magnitude τ = pE sinθ, where θ is the angle between **p** and **E**.
- Expression
**τ** = **p** × **E**
- Name
Potential Energy of an Electric Dipole in Uniform Electric Field
- Note
Minimum energy when **p** is parallel to **E** (θ=0), maximum when anti-parallel (θ=180°).
- Expression
U = -**p** ⋅ **E** = -pE cosθ
Prerequisites
Basic vector algebra (addition, subtraction, components, dot and cross products).
Newton's Laws of Motion (especially F=ma).
Understanding of fundamental forces.
Basic trigonometry.
Common mistakes
Confusing scalar and vector forms of Coulomb's Law and electric field.
Incorrectly applying the principle of superposition (not using vector addition).
Forgetting the inverse square dependence (1/r²) for point charges and inverse cube (1/r³) for dipoles.
Misinterpreting the direction of electric field lines or force on a test charge.
Using distance 'a' instead of '2a' for dipole moment calculations.
Incorrectly calculating the angle for torque or potential energy of a dipole.
Assuming electric field is always zero inside a conductor (it's true only in electrostatic equilibrium).
Keywords
Coulomb's Law
Electrostatic Force
Point Charge
Superposition Principle
Electric Field
Electric Field Lines
Electric Dipole
Electric Dipole Moment
Axial Field
Equatorial Field
Torque on Dipole
Potential Energy of Dipole
Permittivity
Practice preview
Two point charges, +3 microcoulomb and +8 microcoulomb, repel each other with a force of 40 N. If a charge of -5 microcoulomb is added to each of them, what will be the new force between them?…
easy
What is the SI unit of electric field intensity?…
easy
Two point charges, +q and +4q, are placed at a distance 'r' from each other. A third point charge 'Q' is placed on the line joining them such that the net force on 'Q' is zero. What is the position of 'Q' from the charge…
medium