Electric Field Calculator
Calculate the electric field from one or more point charges with magnitude, direction, vector components, step-by-step work, and a visual charge map.
Background
Electric field describes the force per unit positive test charge at a point in space. For point charges, the field depends on charge size, distance, and direction. When several charges are present, the net electric field is found by adding the individual field vectors.
How to use this calculator
- Enter the location of the test point where you want to calculate the electric field.
- Enter each source charge, including its sign, unit, and position.
- Click Calculate Electric Field.
- Review the net electric field magnitude, direction, and components.
- Use the visual charge map to connect the vector calculation to the physical direction.
How this calculator works
- The calculator converts charge values to coulombs and distances to meters.
- For each source charge, it finds the distance from the charge to the test point.
- It calculates the electric field magnitude using Coulomb’s law.
- It determines direction: away from positive charges and toward negative charges.
- It breaks each field vector into x- and y-components.
- It adds all components to find the net electric field.
Formula & Equations Used
Electric field from one point charge: E = k|q| / r²
Coulomb constant: k ≈ 8.99 × 10⁹ N·m²/C²
Vector components: Ex = E cos θ, Ey = E sin θ
Net electric field: Enet = E1 + E2 + E3 + ...
Magnitude of net field: |Enet| = √(Ex2 + Ey2)
Direction angle: θ = atan2(Ey, Ex)
Example Problems & Step-by-Step Solutions
Example 1: Electric field from one positive charge
A +5 μC charge is located 2 m from a test point.
E = k|q| / r²Substitute the values:
E = (8.99 × 10⁹)(5 × 10⁻⁶) / 2²
E ≈ 1.12 × 10⁴ N/C
Because the charge is positive, the field points away from the charge.
Example 2: Electric field from one negative charge
A -3 μC charge is located 1.5 m from a test point.
E = k|q| / r²The magnitude uses the absolute value of charge:
E = (8.99 × 10⁹)(3 × 10⁻⁶) / 1.5²
E ≈ 1.20 × 10⁴ N/C
Because the charge is negative, the field points toward the charge.
Example 3: Net field from two charges
When two charges affect the same point, calculate each field separately.
Then break the fields into components:
Ex,net = Ex,1 + Ex,2
Ey,net = Ey,1 + Ey,2
Finally, use the components to find the net magnitude and direction.
Common mistakes to avoid
- Do not forget to convert microcoulombs to coulombs.
- Do not use the sign of the charge in the magnitude formula; use the sign for direction.
- Do not confuse electric field with electric force. Electric field is measured in N/C.
- Do not add magnitudes directly when directions differ. Add vector components instead.
- Do not calculate the field at the exact location of a point charge.
Frequently Asked Questions
What unit is electric field measured in?
Electric field is usually measured in newtons per coulomb, written as N/C. It can also be written as volts per meter, V/m.
Does a negative charge create a negative electric field?
Not exactly. The field has magnitude and direction. A negative charge makes the electric field point toward the charge.
Why do we add components instead of magnitudes?
Electric field is a vector. If fields point in different directions, their x- and y-components must be added separately.
What happens if the test point is on the charge?
The point-charge formula would divide by zero, so the electric field is undefined at the exact location of a point charge.
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