Force on a Charge
What is an Electric Field?
Imagine you have a magnet and a paper clip. Even without touching them, the magnet can pull the clip. This invisible region of influence around the magnet is similar to an electric field. An electric field is an invisible region around any electrically charged object. It represents the force that would be exerted on other charged objects placed within that region. We say that a charge creates an electric field, and any other charge that enters this field will experience a force. For example, a balloon rubbed on your hair becomes charged and can attract small pieces of paper without touching them—the paper is feeling a force from the balloon's electric field.
The strength of an electric field ($E$) at a point is defined as the force ($F$) per unit charge ($q$) that a small positive test charge would experience at that point. The formula is $E = F / q$. This can be rearranged to give the main formula for force: $F = qE$.
The Fundamental Force Equation: F = qE
The force ($F$) experienced by a charged particle is given by a very simple yet powerful equation:
$F = qE$
Let's break down what each symbol means:
- $F$ is the electric force on the charge. It is measured in Newtons (N), the same unit used for pushes and pulls like weight.
- $q$ is the amount of charge on the particle. It is measured in Coulombs (C). An electron has a charge of about -1.6 x 10-19 C.
- $E$ is the electric field strength. It tells you how strong the field is and is measured in Newtons per Coulomb (N/C).
This equation tells us two very important things:
- Magnitude: The size of the force is directly proportional to both the charge ($q$) and the electric field strength ($E$). Double the charge, and the force doubles. Double the field strength, and the force also doubles.
- Direction: The direction of the force depends on the sign of the charge (positive or negative). A positive charge experiences a force in the same direction as the electric field. A negative charge experiences a force in the opposite direction to the electric field.
Connecting to Coulomb's Law
You might have heard of Coulomb's Law, which describes the force between two specific charges. The force on a charge from an electric field is a more general idea. Think of it this way: Coulomb's Law is used to calculate the electric field created by a specific charge. Once you know that electric field, you can use $F = qE$ to find the force on any other charge you place in it. For a single point charge Q creating the field, the field strength at a distance r is $E = kQ / r^2$, where k is Coulomb's constant[1]. Plugging this into $F = qE$ gives us $F = k q Q / r^2$, which is the familiar Coulomb's Law. So, $F = qE$ is a broader and often more useful way to think about electric force.
| Type of Charge | Direction of Electric Field | Direction of Force Experienced |
|---|---|---|
| Positive (q > 0) | To the right → | To the right → (same direction) |
| Negative (q < 0) | To the right → | To the left ← (opposite direction) |
Forces in Action: From Cathode Ray Tubes to Inkjet Printers
The principle $F = qE$ is not just a formula in a textbook; it is the working principle behind many devices we use or have used.
Example 1: The Old Television (Cathode Ray Tube)
Older televisions and computer monitors used Cathode Ray Tubes (CRTs)[2]. Inside a CRT, a hot filament releases electrons (negative charges). These electrons are accelerated by an electric field ($F = qE$ gives them force, which means acceleration). Then, other electric fields (and magnetic fields) are used to steer the beam of electrons left, right, up, and down to hit specific spots on a phosphor screen, lighting it up to create the picture. The entire image was painted by precisely controlling the force on moving charges!
Example 2: Inkjet Printing
In an inkjet printer, tiny droplets of ink are shot onto the paper. How are they aimed so precisely? The ink droplets are given an electric charge as they leave the print head. They then fly between two metal plates that have an electric field across them. Based on the charge of a droplet, the field exerts a force ($F = qE$) that pushes it left or right, ensuring it lands in the exact correct spot on the page to form a letter or image.
Common Mistakes and Important Questions
Q: If the electric field is zero at a point, is there any force on a charge placed at that point?
A: No. According to the formula $F = qE$, if the electric field $E$ is zero, then the force $F$ must also be zero, regardless of how much charge $q$ the particle has.
Q: Can the force on a negative charge ever be in the same direction as the electric field?
A: No, never. The force on a negative charge is always in the direction opposite to the electric field. This is a fundamental rule derived from the equation $F = qE$. Since $q$ is negative for a negative charge, the force $F$ becomes a negative number times the field vector $E$, which flips its direction.
Q: Is the force $F = qE$ different from the gravitational force on an object?
A: Yes, they are completely different forces. The force $F = qE$ is an electric force that acts only on objects with an electric charge. The gravitational force (weight) acts on anything with mass. For large objects like a person or a book, gravity is much stronger. For tiny particles like electrons, the electric force can be billions of times stronger than gravity.
Footnote
[1] Coulomb's Constant (k): A fundamental constant in electrostatics. Its value is approximately 8.99 x 109 N·m2/C2. It is used in Coulomb's Law to calculate the force between two point charges.
[2] CRT (Cathode Ray Tube): A vacuum tube containing one or more electron guns and a phosphorescent screen, used in older television sets and computer monitors to display images.