Gauss Law
Apply spherical Gauss law to a uniformly charged solid sphere or an ideal infinitely thin charged spherical shell.
Free theory articleApply spherical Gauss law to a uniformly charged solid sphere or an ideal infinitely thin charged spherical shell.
Concept & interpretation
Gauss's Law relates the electric flux through any closed surface (a Gaussian surface) to the net charge enclosed by that surface. For highly symmetric continuous charge distributions like spheres, cylinders, and planar sheets, Gauss's law allows for straightforward calculation of the electric field.
Experiment
You can interact with the Gauss Law module to observe these relationships dynamically.
- Change the Charge distribution to Uniform solid sphere.
- Set the Total charge Q to 1.
- Set the Charge radius R to 1.
- Set the Gaussian radius r to 0.5. Observe the calculated Qenc = 0.125 nC, E = 4.495 N/C, and flux = 4.495π ≈ 14.121459 N·m2/C.
- Change the Gaussian radius r to 2. Since r > R, Qenc now equals the total charge (1 nC), and E = 2.2475 N/C with flux = 35.96π ≈ 112.97167 N·m2/C.
- Change the Charge distribution to Thin spherical shell and set r to 0.5. Notice that Qenc = 0, E = 0, and flux = 0 despite the nonzero total shell charge.