Electric Field of Sphere Calculator

Use this electric field of uniformly charged sphere calculator to calculate electric field of spehere using charge,permittivity of free space (Eo),radius of charged solid spehere (a) and radius of Gaussian sphere.

Electric Field of Uniformly Charged Sphere Calculator
Charge
Permittivity of Free Space (Eo)
Radius of Charged Solid Sphere (a)
Radius of Gaussian Sphere
Electric Field of Sphere (E(r): {{electricFieldSolidSphereResult()}}

How to use Electric Field of Sphere Calculator?

Step 1 - Enter the Charge

Step 2 - Permittivity of Free Space (Eo)

Step 3 - Enter the Radius of Charged Solid Sphere (a)

Step 4 - Enter the Radius of Gaussian Sphere

Step 5 - Calculate Electric field of Sphere

Electric Field of Spehere Formula:

E ( r ) = ( q / ( 4 * π * ε o * $a^3$ ) ) * r

Where,

E(r) = Electric field of sphere

q = Charge

εo= Permittivity of free space

a = Radius of charged solid sphere

r = Radius of gaussian sphere

Frequently Asked Questions

What is a uniformly charged sphere and how does it create an electric field?

A uniformly charged sphere has charge distributed evenly throughout its volume with constant charge density. This sphere creates an electric field that depends on the observation point’s location. Inside the sphere, the field increases linearly with distance from the center (E ∝ r). Outside the sphere, the field decreases as inverse square law (E ∝ 1/r²), identical to a point charge. This sphere is a fundamental model in electrostatics for understanding field configurations.

How does the electric field differ inside and outside a uniformly charged sphere?

Inside the sphere (r < a), only the charge within radius r contributes to the field: E = qr/(4πε₀a³). Outside (r > a), the entire charge Q acts as if concentrated at the center: E = Q/(4πε₀r²). At the surface (r = a), the field is continuous but its derivative (divergence) shows a discontinuity equal to the surface charge density. This transition illustrates Gauss’s law in action.

When should I use this charged sphere model in electrostatics?

Use this model for designing spherical capacitors, analyzing charge distribution effects in conductors, modeling nuclear charge effects on electrons, and understanding electrostatic shielding. It’s foundational for understanding how spherical geometry affects field configuration. Many physical systems approximate spherical symmetry, making this calculation broadly applicable.

What are the key assumptions in uniformly charged sphere calculations?

The model assumes perfect spherical symmetry, uniform charge density throughout the volume, and observation in vacuum or uniform dielectric medium. Real charged spheres may show surface charging or charge redistribution. The sphere is assumed to be isolated (not near other charges). Relativistic effects are neglected for non-relativistic charges.

Uniformly charged sphere calculations extend Coulomb’s law to extended objects with spherical symmetry. By superposition, combinations of spheres can model more complex geometries like spherical shells and concentric spheres. Understanding this case is essential for solving problems involving electric potentials, capacitance calculations, and conductor behavior in electrostatic equilibrium.

Physical Basis & References

This calculator applies Gauss’s Law with Spherical Symmetry:

Inside (r < a): $$E(r) = \frac{qr}{4\pi\varepsilon_0 a^3}$$

Outside (r > a): $$E(r) = \frac{Q}{4\pi\varepsilon_0 r^2}$$

Key Physics Principles:

  • Gauss’s Law - Electric flux through closed surface equals enclosed charge
  • Spherical Symmetry - Field depends only on radial distance
  • Superposition - Total field from all charge elements
  • Boundary Conditions - Field continuous at surface, normal component discontinuous

Key Assumptions:

  • Uniform charge distribution (constant charge density ρ = Q/(4πa³/3))
  • Perfect spherical symmetry
  • Observation point in vacuum (ε₀)
  • Non-relativistic treatment
  • Static conditions

Typical Range of Values:

  • Charge: 1 nC to 1 μC (10⁻⁹ to 10⁻⁶ C)
  • Sphere radius: 1 mm to 1 m
  • Field observation points: inside to several meters away
  • Electric field: 1 N/C to 10⁶ N/C (depending on charge and distance)

Further Reading:

  • Griffiths, D.J. (2013). Introduction to Electrodynamics, 4th Edition. Pearson.
  • Jackson, J.D. (1998). Classical Electromagnetism, 3rd Edition. Wiley.
  • Electrostatics - Hyperphysics (Georgia State University)

Conclusion

You can read more about Electric Field of Uniformly Charged Disk calculator and Antenna Gain Calculator on below links

Read more about other Physics Calculator on below links