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Example: Flux from a Dipole
Suppose you have a two charges, one with value 5μC, the other with value 5μC. There are at separate locations, a distance 1 m apart, and they can be modeled as a dipole. What is the flux through a cylinder with radius 4 m and length 16 m that encloses this dipole?
Facts
- The dipole charges are q=5μC, −q=−5μC.
- The dipole distance is 1 m.
- The cylinder has radius 4 m and length 16 m.
Lacking
- Φe through the cylinder
Approximations & Assumptions
- The axis of the cylinder is aligned with the dipole.
- The dipole and cylinder are centered with respect to each other.
- The electric flux through the cylinder is due only to the dipole (i.e., no other charges exist).
- The charges are point charges, which indeed means we can model them as a dipole.
Representations
Solution
First, notice that