Electric Field of a Point Charge

Electric Field of a Point Charge

The electric field of a point charge is the starting point for nearly all of electrostatics: the field from any real charge distribution can be built up by summing (or integrating) contributions like this one from many point charges. It describes the force per unit charge that a small test charge would feel if placed nearby.This inverse-square relationship — field falling off with the square of distance — shows up throughout physics wherever a quantity radiates outward from a point source, from gravity to light intensity, making the point-charge field a useful mental model well beyond electrostatics.

Coulomb's law gives the field magnitude as E = k·q/r². where k_coul is Coulomb's constant, q_chg is the point charge, r_dist is the distance from the charge, and E_field is the resulting electric field strength.

Apply Coulomb's law directly: the field strength falls off with the square of distance, so doubling the distance quarters the field.

Results

At 10 cm from a modest 2 microcoulomb charge, the field strength is already close to two million volts per meter — a reminder of how strong electric fields can be even from small charges at short range. Because the field drops with the square of distance, moving to twice the distance would cut the field to a quarter of this value, which is why electrostatic hazards are so distance-sensitive.

Assumptions & limitations

• Point charge (or spherically symmetric charge, evaluated outside the sphere).
• Vacuum or air as the surrounding medium.
• No other charges nearby to distort the field.

Related calculations

• Projectile Motion Range
• Kinetic Energy
• Gravitational Potential Energy
• Linear Momentum