Ever wondered why a balloon sticks to your hair or why a lightning bolt zigzags across the sky? That’s electric field and potential at work.
💡 In Simple Words: An electric field is like an invisible wind that pushes charged objects, while electric potential is like the height of a hill that tells you how much energy a charge would gain or lose when it moves.
What is an Electric Field?
An electric field (symbol E) is a region around a charge where another charge would feel a force. Think of it as the way water flows around a rock in a stream – the rock creates a pattern of flow, and a leaf drifting nearby follows that pattern. In the same way, a positive charge creates a field that points outward, and a negative charge creates a field that points inward.
How to calculate it
For a point charge Q, the magnitude of the field at a distance r is given by
E = k · |Q| / r², where k is Coulomb’s constant (≈9×10⁹ N·m²/C²). The direction is away from Q if Q is positive and toward Q if Q is negative.
What is Electric Potential?
Electric potential (symbol V) tells you how much electric potential energy a unit charge would have at a point. Imagine standing on a hill: the higher you are, the more gravitational potential energy you have. Similarly, a point with higher electric potential can give a charge more energy as it moves.
Relation between field and potential
The field and potential are linked. If you move a tiny test charge dq a small distance dl in the direction of the field, the change in potential dV is
dV = -E · dl. The minus sign means the potential drops in the direction the field points, just like you lose height when you walk downhill.
For a point charge, the potential is
V = k · Q / r. Notice the difference: field falls off with r², while potential falls off with r.
Quick Comparison: Electric Field vs. Electric Potential
| Aspect | Electric Field (E) | Electric Potential (V) |
|---|---|---|
| Physical meaning | Force per unit charge (N/C) | Energy per unit charge (J/C or volts) |
| Direction | Vector (has direction) | Scalar (no direction) |
| How it changes with distance | ∝ 1/r² | ∝ 1/r |
| Zero reference | Usually at the charge itself | Often taken at infinity (∞) |
| Analogy | Wind blowing | Height of a hill |
Worked Example
Problem: A point charge of +5 µC is placed at the origin. Find the electric field and potential at a point 0.2 m away on the x‑axis.
Step 1 – Write down the formulas:
- E = k Q / r²
- V = k Q / r
Step 2 – Plug in the numbers (k = 9×10⁹ N·m²/C², Q = 5×10⁻⁶ C, r = 0.2 m):
- E = 9×10⁹ × 5×10⁻⁶ / (0.2)² = 9×10⁹ × 5×10⁻⁶ / 0.04 ≈ 1.125×10⁶ N/C, directed along +x.
- V = 9×10⁹ × 5×10⁻⁶ / 0.2 = 9×10⁹ × 5×10⁻⁶ / 0.2 ≈ 2.25×10⁵ V.
Result: E ≈ 1.13 × 10⁶ N/C to the right, V ≈ 2.25 × 10⁵ V relative to infinity.
Key Points to Remember
- Electric field tells you the direction and strength of the force a charge would feel.
- Electric potential tells you how much energy a charge would have per unit charge at that point.
- E is a vector; V is a scalar.
- For a point charge, E falls off as 1/r² while V falls off as 1/r.
- Use V = -∫E·dl to move between the two concepts.
📝 Likely Exam Questions
- Define electric field and give its SI unit.
Answer: Electric field is the force per unit positive test charge placed in a region; its unit is newton per coulomb (N/C). - State the relationship between electric field and electric potential.
Answer: E = -dV/dx (in one dimension) or vectorially E = -∇V, meaning the field points in the direction of decreasing potential. - Calculate the potential at a distance of 0.1 m from a charge of -2 µC.
Answer: V = kQ/r = 9×10⁹ × (-2×10⁻⁶) / 0.1 = -1.8×10⁵ V. - Two equal positive charges are placed 0.5 m apart. What is the electric field at the midpoint?
Answer: Fields from each charge have equal magnitude kQ/(0.25)² and point opposite, so they cancel; net field = 0 N/C. - Explain why a conductor is an equipotential surface.
Answer: In a conductor free electrons move until the internal electric field is zero; with zero field, there can be no potential difference, so the whole surface shares the same potential.