JEE/NEET Physics · Electrostatics series · Part 3 of 8 · All parts →
- Potential V = energy per coulomb — the ‘electrical height’ of a point (volts)
- V = kQ/r for a point charge — a scalar: add contributions by plain addition, no directions
- Field points ‘downhill’ — from high V to low V; E = −(change in V per metre)
- Potential energy of a charge: U = qV — charge times the landscape’s height
- Positive charges roll downhill (high→low V); negative charges climb (low→high V)
A 9-volt battery, a 220-volt socket, a 25,000-volt TV tube — volts are the everyday face of electric potential. But what IS a volt? The answer turns electricity into a landscape: hills and valleys that charges roll on. Part 3 of the Electrostatics series.
- Volts as electrical height
- What each letter means
- Why potential is a scalar — the gift
- Field and potential: slope and height
- Which way do charges move?
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
Volts as Electrical Height
Potential V at a point = the energy each coulomb would have there:
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| V | electric potential — energy per coulomb at a point | volts (V = J/C) |
| U | potential energy of a charge q placed there: U = qV | joules |
| k, Q, r | Coulomb constant, source charge, distance — as in Part 1 | as before |
Picture it: a positive source charge creates a hill (V high near it, falling off as 1/r); a negative charge creates a valley. Moving a positive charge uphill costs energy; letting it roll downhill releases energy. Every circuit is charges navigating this landscape.
Why Potential Is a Scalar — The Gift
Potential has no direction — just a number at each point. Multiple charges? Add their V’s as plain numbers (+3 V and −5 V give −2 V), no vector triangles. This is why exam problems whisper ‘find the potential’ happily and ‘find the field’ grudgingly — potentials are arithmetic, fields are geometry.
Field and Potential: Slope and Height
The same slope-and-valley relationship as gravity (Gravitation Part 9). Bonus fact this unlocks: inside a charged conductor, V is constant (flat), so E = 0 — the foundation of Part 5’s shielding.
Which Way Do Charges Move?
| Charge | Natural motion | Like a… |
|---|---|---|
| + (positive) | high V → low V (downhill) | ball rolling down |
| − (negative) | low V → high V (uphill!) | bubble rising in water |
The bubble picture for negatives is honest: the electron ‘floats’ up the potential hill because its energy qV falls as V rises (q is negative). This single table explains current direction, battery terminals, and why electrons flow from − to +.
Solved Examples
Direct: V = kQ/r = 9×10⁹ × 3×10⁻⁶ / 0.3 = 9×10⁴ V.
Same spot, E (Part 2): 3×10⁵ N/C — note V and E are different quantities with different behaviours (1/r vs 1/r²). ✔
Answer: V = 90,000 V
Plain addition: V = 9×10⁴ − 4.5×10⁴ = 4.5×10⁴ V. (Fields at that point would need vectors — potentials don’t.)
Energy: U = qV = 0.1 × 4.5×10⁴ = 4,500 J.
✔
Answer: V = 45 kV; U = 4.5 kJ
Work = charge × height climbed: W = qΔV = 2×10⁻⁶ × (900 − 100).
W = 1.6×10⁻³ J.
Check the sign: uphill for a positive charge means WE do positive work — if the question asked the field’s work, it would be −1.6 mJ. ✔
Answer: 1.6 × 10⁻³ J (by the mover)
- Mixing up V (per coulomb) and U (total). V = kQ/r is per coulomb; multiply by the charge you place there to get its energy U = qV.
- Adding potentials as vectors. Never — potentials are scalars; add like bank balances (+ and −).
- Assuming V = 0 means E = 0 (or vice versa). Independent questions! Midpoint between like charges: E = 0 but V ≠ 0. Midpoint of a dipole: V = 0 but E ≠ 0. Both classic MCQs.
- Sign-blindness with ΔV. Write (V_final − V_initial) explicitly; the sign of W = qΔV tells who did the work.
This Physics in Your Daily Life
- Every battery label is this card: a 1.5 V cell gives each coulomb 1.5 joules of hill to spend in your circuit — volts are the currency of electricity.
- The 220 V socket means each coulomb carries 220 J — and why ‘high voltage’ warnings are energy warnings, not force warnings.
- Birds on power lines: a bird touches one wire — both feet at nearly the same potential, so ΔV ≈ 0, no energy drop, no shock. Touch TWO wires and the full landscape hits.
- Defibrillators deliver ~200 J per shock at ~2,000 V — a controlled potential drop through a heart, restarting its rhythm.
- Your phone’s fast charger negotiates higher V for more energy per coulomb-second — USB-PD is literally potential-landscape bargaining.
Practice set (answers hidden — try first)
(NEET-level) V at 0.5 m from a 5 μC charge:
(JEE Main-level) Work to move +3 μC from 50 V to 150 V:
(Concept) Midpoint of a dipole (+q, −q): V and E are:
(NEET-level) A 0.2 C charge at a point with V = 25 V. Its PE:
(Concept) Electrons in a wire drift toward:
- V = kQ/r (scalar)
- U = qV
- E = −dV/dr
- 🔣 V = U/q (volts = J/C); point charge V = kQ/r
- 🔣 potential is a SCALAR — plain addition, no directions
- 🔣 E = −dV/dr: field = the potential’s slope
- 🔣 U = qV for a charge placed in the landscape
- 🔣 + rolls downhill (V falls); − climbs uphill (V rises)
- 🔁 V = U/q; V = kQ/r (scalar sum)
- 🔁 U = qV
- 🔁 E = −dV/dr (slope of V)
- 🧠 Chant: ‘potential is height, field is slope’.
- 🧠 Scalar gift: ‘potentials add like money, fields add like arrows’.
- 🧠 Bubble rule: ‘positives roll downhill, negatives float up’.
- 🏠 Daily: battery labels and socket warnings are joules-per-coulomb in print.
- 🏠 Daily: birds safe on one wire — zero ΔV, zero shock.
Quick revision
- Potential V = energy per coulomb — the ‘electrical height’ of a point (volts)
- V = kQ/r for a point charge — a scalar: add contributions by plain addition, no directions
- Field points ‘downhill’ — from high V to low V; E = −(change in V per metre)
- Potential energy of a charge: U = qV — charge times the landscape’s height
- Positive charges roll downhill (high→low V); negative charges climb (low→high V)
- Volts as electrical height
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