Field Force Charge Two-Factor Scan - Electric Fields & Electrostatics Step by Step

Electric field is force per positive test charge. This page scans force and charge separately before trusting the quotient.

Example

Electric field is force per positive test charge. A reliable page scans force and charge separately before trusting the quotient. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Start with a force and a test charge

A positive test charge marks point P. The diagram binds the test charge to 3 coulombs and the force arrow to 12 newtons.

q_{\text{test}}=3\ \text{C}\qquad F=12\ \text{N}

Compute force per coulomb

Electric field is not the whole force. It is the force assigned to each coulomb of positive test charge at the point.

E=\frac{F}{q_{\text{test}}}

Divide the checked quantities

Dividing 12 newtons by 3 coulombs gives 4 newtons per coulomb.

E=\frac{12\ \text{N}}{3\ \text{C}}=4\ \text{N/C}

Scan force while charge stays fixed

Hold the test charge at 3 coulombs. Three force rows make the direct relation visible: more force means more newtons per coulomb.

\begin{array}{c|c|c}F&q_{\text{test}}&E\\6\ \text{N}&3\ \text{C}&2\ \text{N/C}\\12\ \text{N}&3\ \text{C}&4\ \text{N/C}\\18\ \text{N}&3\ \text{C}&6\ \text{N/C}\\\end{array}

Scan charge while force stays fixed

Now hold the force at 12 newtons. More test charge spreads the same force over more coulombs, so the field value falls.

\begin{array}{c|c|c}F&q_{\text{test}}&E\\12\ \text{N}&2\ \text{C}&6\ \text{N/C}\\12\ \text{N}&3\ \text{C}&4\ \text{N/C}\\12\ \text{N}&6\ \text{C}&2\ \text{N/C}\\\end{array}

electrostatics Use separate rows for the force numerator and the charge denominator.