Quickly calculate the electric field strength of a uniformly charged sphere at any point. Our tool simplifies complex electrostatics calculations, whether you're inside, on the surface, or outside the sphere. Understand the core principles of Coulomb's Law and Gauss's Law with this essential physics calculator.
Formula:
Electric Field Formulas for a Uniformly Charged Sphere
The electric field (E) of a uniformly charged sphere depends on the distance (r) from its center relative to the sphere's radius (R). The formulas derive from Gauss's Law.
- Inside the sphere (r < R):
E = (k × Q × r) / R3 - On or Outside the sphere (r ≥ R):
E = (k × Q) / r2
Where:
- E = Electric Field Strength (Newtons per Coulomb, N/C, or Volts per meter, V/m)
- k = Coulomb's Constant ≈ 8.9875 × 109 N·m2/C2
- Q = Total Charge of the Sphere (Coulombs, C)
- r = Distance from the center of the sphere to the point of interest (meters, m)
- R = Radius of the Sphere (meters, m)
Note: At the exact center (r=0), the electric field is zero.