Calculate Electric Force If Electron Put in at Point B

When an electron is placed at point B in an electric field, the electric force acting on it can be calculated using Coulomb's Law. This calculation is fundamental in understanding electrostatic interactions and is widely used in physics and engineering.

Introduction

Electric force is a fundamental concept in physics that describes the interaction between charged particles. When an electron is placed at point B, the force it experiences depends on the charges of the electron and the source charge, as well as the distance between them.

Coulomb's Law provides the mathematical relationship between these factors, allowing us to quantify the electric force. This calculation is essential in various fields, including electronics, materials science, and astrophysics.

Coulomb's Law

Coulomb's Law states that the magnitude of the electric force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them. The formula is:

Formula

F = k · (|q₁q₂| / r²)

Where:

F = Electric force (N, Newtons)
k = Coulomb's constant (8.9875 × 10⁹ N·m²/C²)
q₁ = Charge of first particle (C, Coulombs)
q₂ = Charge of second particle (C, Coulombs)
r = Distance between charges (m, meters)

For an electron placed at point B, we typically consider the electron's charge (q₁ = -1.602 × 10⁻¹⁹ C) and the charge of the source (q₂). The distance r is the separation between the electron and the source charge.

Note

The direction of the electric force is along the line connecting the two charges. If both charges are of the same sign, the force is repulsive; if they are of opposite signs, the force is attractive.

Examples

Let's consider two scenarios where an electron is placed at point B:

Example 1: Electron near a Proton

If an electron is placed 1 nm (1 × 10⁻⁹ m) from a proton (charge q₂ = +1.602 × 10⁻¹⁹ C), the electric force can be calculated as follows:

Calculation

F = (8.9875 × 10⁹ N·m²/C²) · (|(-1.602 × 10⁻¹⁹ C)(1.602 × 10⁻¹⁹ C)| / (1 × 10⁻⁹ m)²)

F = (8.9875 × 10⁹) · (2.566 × 10⁻³⁸ / 1 × 10⁻¹⁸)

F = (8.9875 × 10⁹) · (2.566 × 10⁻²⁰)

F ≈ 2.29 × 10⁻¹⁰ N

The attractive force between the electron and proton is approximately 2.29 × 10⁻¹⁰ N.

Example 2: Electron near Another Electron

If an electron is placed 1 nm from another electron, the electric force is:

Calculation

F = (8.9875 × 10⁹ N·m²/C²) · (|(-1.602 × 10⁻¹⁹ C)(-1.602 × 10⁻¹⁹ C)| / (1 × 10⁻⁹ m)²)

F = (8.9875 × 10⁹) · (2.566 × 10⁻³⁸ / 1 × 10⁻¹⁸)

F = (8.9875 × 10⁹) · (2.566 × 10⁻²⁰)

F ≈ 2.29 × 10⁻¹⁰ N

The repulsive force between two electrons is approximately 2.29 × 10⁻¹⁰ N.

FAQ

What is Coulomb's Law?

Coulomb's Law is a fundamental principle in physics that describes the electrostatic force between two point charges. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

How do I calculate the electric force between two charges?

Use the formula F = k · (|q₁q₂| / r²), where k is Coulomb's constant, q₁ and q₂ are the charges, and r is the distance between them. The result will be in Newtons (N).

What units should I use for the calculation?

Use Coulombs (C) for charge, meters (m) for distance, and the result will be in Newtons (N). For very small distances like nanometers, convert to meters (1 nm = 1 × 10⁻⁹ m).

Is the electric force always attractive or repulsive?

The force is attractive if the charges have opposite signs and repulsive if they have the same sign. The magnitude is always calculated using Coulomb's Law.