Suppose you have a two charges, one with value $5 \mu\text{C}$, the other with value $5 \mu\text{C}$. There are at separate locations, a distance $1 \text{ m}$ apart, and they can be modeled as a dipole. What is the flux through a cylinder with radius $4 \text{ m}$ and length $16 \text{ m}$ that encloses this dipole?

• The dipole charges are $q=5 \mu\text{C}$, $-q=-5 \mu\text{C}$.
• The dipole distance is $1 \text{ m}$.
• The cylinder has radius $4 \text{ m}$ and length $16 \text{ m}$.

• $\Phi_e$ through the cylinder

• 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.

• We represent the situation with the following diagram.

First, notice that