What is the electric field magnitude at distance r from a point charge q?

What is the electric field magnitude at distance r from a point charge q?

• A. E = k q / r^2
• B. E = k q r^2
• C. E = (1/(4π ε0)) q / r
• D. E = k / r^2

Answer: (A)

A point charge creates a radial electric field whose magnitude falls off with the square of the distance from the charge. The correct expression for the magnitude is E = k |q| / r^2, where k is Coulomb’s constant (k = 1/(4π ε0)). This 1/r^2 dependence comes from the field lines spreading over the surface area of a sphere, which grows as 4π r^2, so the field strength must decrease proportional to 1/r^2 to keep the total flux constant. The sign of q sets the direction (away from the charge if q is positive, toward it if q is negative), but the magnitude is the positive quantity given by the formula. The other forms don’t match this distance dependence or omit the charge factor, so they don’t represent the correct magnitude.

A point charge creates a radial electric field whose magnitude falls off with the square of the distance from the charge. The correct expression for the magnitude is E = k |q| / r^2, where k is Coulomb’s constant (k = 1/(4π ε0)). This 1/r^2 dependence comes from the field lines spreading over the surface area of a sphere, which grows as 4π r^2, so the field strength must decrease proportional to 1/r^2 to keep the total flux constant. The sign of q sets the direction (away from the charge if q is positive, toward it if q is negative), but the magnitude is the positive quantity given by the formula. The other forms don’t match this distance dependence or omit the charge factor, so they don’t represent the correct magnitude.