Electric Field LinesJEE Main

Field & potential around point charges — interactive Physics simulation for IIT-JEE.

Concept

An electric field $\vec E$ is the force per unit positive test charge. Field lines point away from positive charges and into negative ones; their density encodes field strength. The potential $V$ is the scalar work per unit charge — a single number at each point whose negative gradient is the field.

Key formula

\vec E = \frac{kq}{r^2}\hat r, \quad V = \frac{kq}{r}, \quad F = \frac{kq_1 q_2}{r^2}

Derivation

Coulomb's law gives the force between charges, $F = kq_1q_2/r^2$ with $k = 8.99\times10^9\,\text{N·m}^2/\text{C}^2$ . Dividing by a test charge defines the field $E = kq/r^2$ .

Fields superpose vectorially: the total field is the vector sum of each charge's contribution. Potentials superpose as scalars: $V = \sum kq_i/r_i$ .

A null point is where the vector fields cancel. For two like charges it lies between them; for unlike charges it lies outside, beyond the weaker charge.

Scenarios to explore

Electric Field Lines — Field & potential around point charges.

Real-world applications

Capacitors, where a near-uniform field stores energy.
Cathode-ray and ink-jet deflection.
Shielding and the behaviour of conductors in fields.

JEE exam tips

Use symmetry first — many midpoint fields cancel or double cleanly.
$\vec E = -\nabla V$ : field points from high to low potential.

Common mistakes

Adding potentials as vectors or fields as scalars — it is the other way around.
Forgetting the field is zero inside a conductor in electrostatic equilibrium.
Dropping the sign of the charge when summing potentials.

Exam traps to avoid

Two unlike charges have a null point in potential (V = 0 surface) but no field null between them.
Field lines never cross and are always perpendicular to conductor surfaces.