Why electric fields matter in everyday life
Ever felt a static shock after rubbing a balloon on your hair? That tiny jolt is an electric field at work, nudging electrons from one place to another.
In simple words, an electric field is a region where a charge feels a push or pull. Electric potential tells you how much energy a charge would have if it were placed there.
What is an electric field?
An electric field (symbol E) is a vector quantity – it has both size and direction. Think of it like water flowing through a pipe: the water’s speed tells you how strong the flow is, and the direction tells you where it’s going. A positive test charge placed in that flow would be pushed along the same direction.
Direction and strength
- Direction: points away from positive charges and toward negative charges.
- Strength: measured in newtons per coulomb (N·C⁻¹). The closer you are to a charge, the stronger the field.
What is electric potential?
Electric potential (symbol V or sometimes φ) is a scalar – it only has size, no direction. Imagine a hill: the height of the hill tells you how much potential energy a ball would have at that spot. Similarly, the electric potential tells you how much energy per unit charge is stored at a point.
Potential difference (voltage)
The difference in potential between two points is called voltage. It’s what makes current flow, just like water flows from a higher to a lower level.
Relationship between field and potential
The electric field is the rate of change of potential with distance. In one‑dimensional form, E = -dV/dx. The minus sign means the field points from high potential to low potential, just as water flows downhill.
Worked example
Problem: A uniform electric field of 500 N·C⁻¹ points from left to right. What is the potential difference between two points 0.10 m apart along the field direction?
Solution:
- Use the relation ΔV = -E·d, where d is the distance along the field.
- Plug in the numbers: ΔV = -(500 N·C⁻¹)(0.10 m) = -50 V.
- The negative sign tells us the point on the right is at a lower potential than the left.
So the two points differ by 50 volts.
Quick comparison
| Aspect | Electric Field (E) | Electric Potential (V) |
|---|---|---|
| Nature | Vector (has direction) | Scalar (no direction) |
| Unit | newton per coulomb (N·C⁻¹) | volt (V) = joule per coulomb (J·C⁻¹) |
| What it tells you | Force a charge would feel | Energy per unit charge stored at a point |
| How they relate | E = -dV/dx (gradient of V) | V = -∫E·dl (area under E‑vs‑distance curve) |
📝 Likely Exam Questions
- Q1: Define electric field and state its SI unit.
A: Electric field is the force per unit positive charge at a point; unit = N·C⁻¹. - Q2: A point charge of +2 µC creates a field of 9×10⁵ N·C⁻¹ at 0.02 m. Find the potential at that distance.
A: V = k·q/r = (9×10⁹)(2×10⁻⁶)/0.02 = 9×10⁵ V. - Q3: Explain why electric field lines never cross each other.
A: If they crossed, a point would have two different directions for the field, which is impossible because the field has a single direction at any location. - Q4: A uniform field of 200 N·C⁻¹ exists between two parallel plates 5 cm apart. Calculate the potential difference.
A: ΔV = E·d = 200 × 0.05 = 10 V. - Q5: Sketch a simple diagram showing the direction of electric field lines around a positive charge and label the potential gradient.
A: (Answer expects a radial outward field with potential decreasing outward; gradient points opposite to field lines.)