Electrostatic Potential: Point Charges, Potential Energy & Field Relation: quick revision, 15 bites

Potential Is Work Per Unit Charge

Potential = work done per charge.

Takeaway. Potential is a scalar property of the field; potential energy depends on the charge placed in it.

Potential of a Point Charge

One charge, one simple formula.

Takeaway. Potential is a scalar 1/r quantity — much easier to add than the vector field.

Potential Energy and Potential Difference

Charge × potential = energy stored.

Potential energy is **charge times potential**; potential difference is **work per unit charge** between two points.

Takeaway. U scales with the test charge q; V does not — V belongs to the field, U belongs to the charge-field system.

Superposition: Add Potentials, Not Fields

Potentials add like plain numbers.

Takeaway. Because V is a scalar, superposition is simple algebraic addition — no vector components needed.

Midpoint of Equal & Opposite Charges

Two opposite charges cancel at midpoint.

Takeaway. Zero potential does NOT mean zero field — the field at the midpoint of a dipole is non-zero and points from + to −.

Midpoint of Two Equal Positive Charges

Same sign? Potentials double up.

Takeaway. Same-sign charges reinforce potential; opposite-sign charges cancel it at the midpoint.

Zero Potential ≠ Zero Field

V = 0 does not mean E = 0.

Takeaway. V and E are related by a derivative — one can be zero while the other is not.

Potential Is the Negative Integral of Field

Field is the slope of potential.

Takeaway. The negative sign means potential drops in the direction of the field.

Potential vs Electric Field

Scalar vs vector — know the difference.

Takeaway. V is easier to compute (scalar); E carries direction and is the gradient of V.

Remember the 1/r vs 1/r² Rule

Potential is one power softer.

Takeaway. Anything derived from potential (energy) goes as 1/r; anything derived from field (force) goes as 1/r².

Sign Discipline in Numericals

Signs decide the marks.

Takeaway. Most lost marks in potential problems come from dropped signs, not wrong formulas.

Why Potential Matters in Circuits

Batteries rate potential, not field.

A 9 V battery maintains a **potential difference** of 9 V between its terminals. Current flows because charges move from high to low potential — the field does the pushing, but potential is what we measure and rate.

Takeaway. Voltage is potential difference — the practical face of electrostatic potential.

Fast Route for Multi-Charge Potential Problems

Skip vectors — just add scalars.

Takeaway. If the question asks only for V, never decompose into components — that's wasted effort.

Potential Is Continuous Everywhere

No jumps in V, ever.

Unlike electric field, which can jump across a charged surface, **potential is continuous everywhere** in space (except exactly at a point charge). This is why V is often easier to work with than E.

Takeaway. Continuity of V makes it a safer quantity to compute and match across regions.

The Volt Is Named After Alessandro Volta

One volt, one inventor's name.

The unit of potential, the **volt (V)**, honours Alessandro Volta, inventor of the voltaic pile — the first chemical battery. One volt = one joule per coulomb.

Takeaway. 1 V = 1 J/C — the unit itself encodes the definition of potential.