# How to Determine the Direction & Magnitude of the Electric Field

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An electric field is described as a field surrounding an electrically charged particle that exerts a force on other electrically charged particles. It is also a vector quantity, meaning that it has direction in addition to magnitude. The magnitude of the electric field varies at a distance, d, from the charge based on the charge of the respective particle. Therefore, the electric field for a single point charge can easily be calculated from these measured values.

### Things You'll Need

• Scientific calculator
• Identify the charge and distance from the charge required for the electric field calculation. For example, assume a question asks for the direction and magnitude of an electric field 1.2 meters away from a point charge of 2.0 x 10^-9 coulombs.

• Substitute these values into the electric field equation. This equation identifies the electric field as the product of the electrical constant K (9.0 x 10^9 N*m^2/C^2) and the charge, q, divided by the square of the distance, d, from the charge. Thus, the calculation using the previous example would give an electric field magnitude of 7.5 newtons per coulomb.

E = (K*q ) / d^2

E = [(9.0 x 10^9 Nm^2/C^2)(1.2 x 10^-9 C)] / (1.2^2)

E = 7.5 N/C

• Identify the direction based on the charge. The electric field points outward from a positive, and inward from a negative. Thus, the example problem would have a final electric field 1.2 meters away equal to 7.5 N/C outward.

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