The electric field is the influence a charge creates around itself that can exert forces on other charges.
We already know that free electrons exist and have a negative charge. We also know that charges of the same sign repel each other and charges of opposite sign attract each other.
But in engineering, saying “they attract a lot” or “they attract a little” isn’t enough. We need to quantify that force. And, above all, we need to answer a troubling question:
If two charges aren’t touching… how does one know the other is there? How is that force transmitted through a vacuum?
Welcome to the world of Fields.
Coulomb’s Law
At the end of the 18th century, Charles-Augustin de Coulomb accurately measured the force between electric charges and stated the law that bears his name.
It is the foundation of all electrostatics and looks suspiciously similar to Newton’s Law of Universal Gravitation. The Coulomb’s Law states:
Let’s break down this formula, because it tells us much more than it seems:
(force): The magnitude of the attraction or repulsion force (in newtons). Its direction lies along the line joining the charges. and (charges): The amount of charge on each body (in coulombs). The larger the charges, the greater the force. (distance squared): The force is inversely proportional to the square of the distance. If you double the separation between charges, the force becomes one-fourth. (Coulomb’s constant): Depends on the medium. In a vacuum, . At the particle scale, the electrical interaction is vastly stronger than the gravitational one.
Coulomb’s law and Newton’s law of gravitation both share a
The Concept of Field
Speaking only of forces between two bodies suggests an uncomfortable “action at a distance.” Faraday and Maxwell developed the concept of a field to describe the physical influence present at every point in space.
Imagine a trampoline.
- If you place a bowling ball in the center, the fabric deforms.
- If you then roll a marble, the marble moves toward the ball not because the ball “pulls” it, but because it follows the curvature of the fabric.
In electricity, that fabric, that vector quantity, is the electric field.
- An electric charge creates a field around it.
- Any other charge entering that space will feel a force.
The Electric Field (E)
We define the electric field (represented by the letter
Or, using Coulomb’s Law:
Notice the difference:
- Force (F) requires two charges (the one pushing and the one being pushed).
- The Field (E) only requires one source charge. The field exists even if no one is there to feel it. It is a property of space.
Field Lines
Since the field is invisible, we use Field Lines to visualize it. They are imaginary arrows that tell us which way a positive charge would be propelled.
- They emanate from Positive charges (sources).
- They terminate at Negative charges (sinks).
- They never cross.
- Where the lines are closer together, the field is stronger.
Relationship Between Field and Potential
Here comes the idea that will connect us to the next article.
The unit of the electric field is the newton per coulomb (N/C): it indicates the force that would act per unit charge.
But this unit is equivalent to another you will use much more often: volts per meter (V/m).
This unit equivalence reflects a deeper relationship: the electric field points in the direction where the potential decreases most rapidly. In one dimension, it is expressed as
Imagine the space between two charged plates, like in a capacitor:
- Between two parallel plates, we can approximate
. Therefore, a large potential difference over a small distance produces a very intense field. - If that field becomes too strong for the material in between (air, plastic), it will forcibly strip electrons and create a spark.
This is why you cannot bring high-voltage wires too close together. Even if they don’t touch, the Electric Field (V/m) in the intervening air can become so high that the air becomes a conductor (electric arc).
