The boundary condition on E isSelect one:a. E1 = E2b. an×(E1− E2) = 0c. None of aboved. an•(E1− E2) = 0

To determine the correct boundary condition on the electric field $\mathbf{E}$, we need to examine what each option represents in the context of electromagnetic theory.

1. Option A: $E_1 = E_2$
   This suggests that the electric fields on either side of the boundary are equal. This condition is true in certain cases, such as in the case of perfect electric conductors, but it is not the general boundary condition applicable for all scenarios.

2. Option B: $\mathbf{a}_n \times (\mathbf{E}_1 - \mathbf{E}_2) = 0$
   This indicates that the vector cross product of the normal vector $\mathbf{a}_n$ and the difference in electric fields is zero. A cross product being zero implies that $\mathbf{E}_1 - \mathbf{E}_2$ is parallel to $\mathbf{a}_n$, which would not typically be the case for normal components across dielectrics or conductors.

3. Option C: None of the above.
   This option remains to be evaluated after our analysis of the first two.

4. Option D: $\mathbf{a}_n \cdot (\mathbf{E}_1 - \mathbf{E}_2) = 0$
   This states that the dot product of the normal vector and the difference of the electric fields is zero, which means that the normal components of the electric fields are continuous across the boundary under typical boundary conditions in electromagnetism.

Conclusion:

For the boundary conditions of the electric field at the interface between two media, the correct condition is that the normal component of the electric field is continuous across the boundary, given by

$\mathbf{a}_n \cdot (\mathbf{E}_1 - \mathbf{E}_2) = 0$

Thus, the correct answer is Option D.