(a) Why two electric lines of force/field cannot intersect each other ?
(b) State Coulomb's law, explain its vector form and define S.I unit of electric charge. State two limitations of Coulomb's law.

**OR**

(a) What is the shape of equipotential surface for a given point charg

Question

(a) Why two electric lines of force/field cannot intersect each other ?
(b) State Coulomb's law, explain its vector form and define S.I unit of electric charge. State two limitations of Coulomb's law.

**OR**

(a) What is the shape of equipotential surface for a given point charge q.
(b) State Gauss's theorem. With the help of diagram, derive an expression for the electric field intensity due to uniformly charged thin spherical shell at a point (i) outside (ii) inside (iii) on the surface of the spherical shell.

Accepted Answer

>

> [!TLDR]
> Field lines can't cross because the field direction at any point must be unique; Coulomb's law gives the force between two point charges as $\vec F=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1q_2}{r^2}\hat r$, with SI unit of charge the coulomb, and it's strictly valid only for point charges at rest in vacuum/a defined medium.
>
> **(a) Why field lines cannot intersect:** The tangent to an electric field line at any point gives the direction of the net electric field at that point. If two field lines were to cross at a point, the field at that point would have to point in two different directions simultaneously — which is impossible, since the net electric field at any given point is a single, unique vector (found by vector-adding all contributions there). Hence electric field lines never intersect.
>
> **(b) Coulomb's law:** The electrostatic force between two point charges $q_1$ and $q_2$ separated by a distance $r$ (in vacuum) is directly proportional to the product of the charges and inversely proportional to the square of the distance between them, and acts along the line joining them:
> $$F=\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r^2}$$
> where $\varepsilon_0$ is the permittivity of free space.
>
> **Vector form:** if $\hat r_{21}$ is the unit vector from charge 2 to charge 1, the force on charge 1 due to charge 2 is:
> $$\vec F_{12}=\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r^2}\hat r_{21}$$
> This vector form automatically gives an attractive force (pointing toward the other charge) for unlike charges (product $q_1q_2<0$), and a repulsive force (pointing away) for like charges (product $q_1q_2>0$), consistent with Newton's third law: $\vec F_{12}=-\vec F_{21}$.
> …

Q.(a) Why two electric lines of force/field cannot intersect each other ?

Concept understanding — Coulomb Force Superposition

Coulomb Force Superposition – From Intuition to Precision

The Precise Statement

Why This Matters (and a Common Trap)

The Deeper Reason

Why this formula?

Coulomb Force Superposition — Why the Formula Holds

The Key Formula

Why This Works — The Physical Reasoning

1. Coulomb's Law is a Two-Body Interaction

2. Forces Add as Vectors (Newton's Third Law + Linearity)

3. The Electric Field is Linear

The Crucial Assumption (Why It's Not Trivial)

Q.(a) Why two electric lines of force/field cannot intersect each other ?

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