Electric Field Calculator

A point charge creates an electric field that weakens with the square of distance.

How the Math Works

The Electric Field Calculator uses Coulomb's Law to determine the electric field strength (E) generated by a point charge (Q) at a given distance (r). The formula E = k·Q ÷ r² shows that the field strength is directly proportional to the charge and inversely proportional to the square of the distance from the charge. Coulomb's constant (k ≈ 8.988×10⁹ N·m²/C²) scales the equation to match SI units. This relationship means doubling the charge doubles the field strength, while doubling the distance reduces the field by a factor of four, highlighting the rapid decrease in field strength with distance.

Practical Applications

To apply this calculation, input the charge (Q) in coulombs and the distance (r) in meters from the charge to the point of interest. The calculator computes the electric field magnitude in newtons per coulomb (N/C), which is critical for determining forces on other charges, designing capacitors, or analyzing electrostatic systems. Engineers use it to ensure electronic components withstand electric forces, while physicists apply it to study particle interactions. For example, calculating the field around a charged sphere helps predict how nearby objects will behave in that field.

Day-to-Day Use

This calculation underpins technologies we encounter daily, from the static electricity causing small shocks when touching metal doorknobs to the operation of touchscreens that detect finger capacitance. It also explains why lightning rods protect buildings by channeling electric fields to the ground. Understanding electric fields helps in designing safer electrical systems, such as power lines and household appliances, and even in medical imaging technologies like MRI machines, which rely on strong, controlled electric and magnetic fields.

Worked example

1 µC at 0.5 m → about 35,950 N/C.

FAQ