When a sphere encloses an electric dipole, the net electric flux through the sphere is zero.
Key Concept (Gauss’s Law):
- According to Gauss’s Law, the total electric flux through a closed surface is proportional to the net charge enclosed:
Φ = Q_enclosed / ε₀
Understanding the Dipole:
- An electric dipole consists of two equal and opposite charges: +q and -q.
- When both charges are inside the sphere:
- Net charge enclosed = +q + (-q) = 0
Result:
- Since the net enclosed charge is zero, the total electric flux through the sphere is also zero.
Important Insight:
- Even though the net flux is zero, the electric field is not zero at every point on the surface.
- Field lines enter and leave the surface, but they cancel out overall.
Visual Understanding:
- The number of electric field lines entering the sphere equals the number leaving it.
Exam Tip:
- Always focus on net enclosed charge, not individual charges.
- For a dipole inside a closed surface → Net flux = 0