An arbitrary surface encloses an electric dipole. What is electric flux passing through the surface?

The electric flux through a closed surface surrounding an electric dipole is determined by the net charge enclosed within that surface. Since an electric dipole consists of two equal and opposite charges, the total charge is zero.

Understanding Electric Flux

Electric flux is a measure of the electric field passing through a given area. It is calculated using the formula:

• Φ = ∮ E · dA

Where:

• Φ is the electric flux.
• E is the electric field.
• dA is the differential area vector.

Applying Gauss's Law

According to Gauss's Law, the electric flux through a closed surface is proportional to the enclosed charge:

• Φ = Q_enc / ε₀

Here, Q_enc is the enclosed charge and ε₀ is the permittivity of free space.

Result for the Dipole

Since the dipole has no net charge (Q_enc = 0), the electric flux through the surface is:

This means that the total electric flux passing through any closed surface enclosing an electric dipole is zero.