If there is no free surface charge at a boundary, what is the relation between the normal components of D on both sides?

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Multiple Choice

If there is no free surface charge at a boundary, what is the relation between the normal components of D on both sides?

Explanation:
The normal component of the electric displacement D changes only when there is free charge at the boundary. Gauss’s law for D gives the relation D2_n − D1_n = σ_free, so if there is no free surface charge (σ_free = 0) the jump is zero and the normal components must be equal on both sides. This reflects that D is defined to incorporate free charges, while bound charges from polarization are handled within the material’s response. Therefore, D2_n = D1_n holds.

The normal component of the electric displacement D changes only when there is free charge at the boundary. Gauss’s law for D gives the relation D2_n − D1_n = σ_free, so if there is no free surface charge (σ_free = 0) the jump is zero and the normal components must be equal on both sides. This reflects that D is defined to incorporate free charges, while bound charges from polarization are handled within the material’s response. Therefore, D2_n = D1_n holds.

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