The boundary condition on E isSelect one:a. an•(E1− E2) = 0b. None of abovec. E1 = E2d. an×(E1− E2) = 0

To determine the correct boundary condition on the electric field $\mathbf{E}$, we need to analyze the options provided.

1. Understanding Boundary Conditions: The boundary conditions on the electric field at the interface between two media dictate how the electric field behaves across the boundary.

2. Analyzing Options:

   • a. $\mathbf{a_n} \cdot (\mathbf{E_1} - \mathbf{E_2}) = 0$: This suggests that the component of the electric field difference normal to the boundary is zero. This condition usually applies for perfect electric conductors.
   • b. None of the above: We will consider this if none of the other options accurately describe the boundary condition.
   • c. $\mathbf{E_1} = \mathbf{E_2}$: This suggests that the electric fields on either side of the boundary are equal, which is typically valid under certain conditions such as at the surface of a dielectric.
   • d. $\mathbf{a_n} \times (\mathbf{E_1} - \mathbf{E_2}) = 0$: This means that the component of the electric field difference tangential to the boundary is zero, which is generally true at a boundary.

3. Conclusion: The correct boundary condition on the electric field at the interface between two different media is that the tangential components of the electric field must be continuous, leading us to option d.

Final Answer

d. $\mathbf{a_n} \times (\mathbf{E_1} - \mathbf{E_2}) = 0$