Calculating Electric Field Strength
An electric field is a field that exerts a force on charges – attracting or repelling them. Moreover, every single charge generates its own electric field. That's why, for example, two electrons with the elementary charge e = 1.6 × 1 0 − 19 C e=1.6×10 −19 C repel each other. You can check our Coulomb's law calculator if you want to quantify the amount of electric force between two charged particles.
You probably know that everything in nature is made of atoms, which consist of a nucleus (positive charge) and electrons orbiting around the nucleus (negative charge). The nucleus generates an electric field that attracts and holds electrons in their orbits, just like the sun and the planets around it.
Electric field equation
You can estimate the electric field created by a point charge with the following electric field equation:
\[ E = \frac{kQ}{r^2} \]
where:
- E – Magnitude of the electric field;
- Q – Charge point;
- r – Distance from the point; and
- k – Coulomb's constant:
\[ k = \frac{1}{4\pi \epsilon_0} = 8.9876 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2 \]
where ε 0 is vacuum permittivity.
You can check with our electric field calculator that the magnitude of the electric field decreases rapidly as the distance from the charge point increases.
Example
Calculating Electric Field Strength
The electric field strength refers to the force per unit charge experienced by a small positive test charge placed in the field. It is a vector quantity, which means it has both magnitude and direction.
The general approach to calculating electric field strength includes:
- Identifying the charge generating the electric field.
- Knowing the distance from the charge where the field is being measured.
- Applying the electric field formula to calculate the field strength.
Electric Field Strength Formula
The general formula for electric field strength is:
\[ E = \frac{{kQ}}{{r^2}} \]Where:
- E is the electric field strength (in N/C).
- k is Coulomb's constant, \( 8.9876 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \).
- Q is the charge creating the electric field (in C).
- r is the distance from the charge where the field is being measured (in meters).
Example:
If a point charge of \( 2 \, \mu\text{C} \) is placed at the origin and the distance from the charge to the point where the electric field is being measured is 0.5 meters, the electric field strength is:
- Step 1: Use the electric field formula: \( E = \frac{{(8.9876 \times 10^9)(2 \times 10^{-6})}}{{(0.5)^2}} \).
- Step 2: Calculate the result: \( E = \frac{{(8.9876 \times 10^9)(2 \times 10^{-6})}}{{0.25}} = 71.9 \times 10^3 \, \text{N/C} \).
Electric Field Due to Multiple Charges
When multiple charges are present, the electric field at any point is the vector sum of the fields due to each individual charge. The direction of the electric field depends on the sign of the charge.
Example:
If there are two charges, \( +3 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \), separated by 1 meter, the net electric field at the midpoint is the result of the vector sum of the fields due to both charges:
- Step 1: Calculate the electric field due to each charge using the formula \( E = \frac{{kQ}}{{r^2}} \).
- Step 2: Sum the fields taking into account the direction of the fields from each charge.
Real-life Applications of Electric Field Strength
Electric field strength has many practical applications, such as:
- Determining the forces on charges in an electric field.
- Designing capacitors and other electrical components in circuits.
- Understanding the behavior of charges in various physical systems (e.g., electron movement in semiconductors).
Common Units of Electric Field Strength
SI Unit: The unit of electric field strength is Newtons per Coulomb (N/C).
The value of Coulomb's constant is \( k = 8.9876 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \), and the electric field is measured in N/C.
Common Operations with Electric Field Strength
Electric Field due to Point Charge: The electric field strength depends on the magnitude of the charge and the distance from it.
Superposition Principle: When multiple charges are involved, the electric field strength at a point is the vector sum of the individual fields from all charges.
Electric Field Lines: The electric field lines indicate the direction and magnitude of the electric field. They radiate outward from positive charges and inward toward negative charges.
| Problem Type | Description | Steps to Solve | Example |
|---|---|---|---|
| Electric Field of a Point Charge | Finding the electric field strength created by a point charge at a certain distance from it. |
|
If a point charge of \( 5 \, \mu\text{C} \) is located at a distance of \( 2 \, \text{m} \), the electric field strength is \( E = \frac{{(8.99 \times 10^9)(5 \times 10^{-6})}}{{2^2}} = 1123.75 \, \text{N/C} \). |
| Electric Field of a Uniformly Charged Plane | Finding the electric field strength due to a uniformly charged plane. |
|
If the surface charge density is \( 1.5 \, \mu\text{C/m}^2 \), the electric field strength is \( E = \frac{{1.5 \times 10^{-6}}}{{2(8.85 \times 10^{-12})}} = 84,835 \, \text{N/C} \). |
| Electric Field of a Dipole | Finding the electric field strength at a point along the axis of a dipole. |
|
If the dipole moment is \( 3 \times 10^{-29} \, \text{C} \cdot \text{m} \) and the distance is \( 1 \, \text{m} \), the electric field strength is \( E = \frac{{2(8.99 \times 10^9)(3 \times 10^{-29})}}{{1^3}} = 5.39 \times 10^{-19} \, \text{N/C} \). |
| Electric Field in a Parallel Plate Capacitor | Finding the electric field strength between the plates of a parallel plate capacitor. |
|
If the voltage between the plates is \( 500 \, \text{V} \) and the separation distance is \( 0.02 \, \text{m} \), the electric field strength is \( E = \frac{{500}}{{0.02}} = 25,000 \, \text{N/C} \). |
