Question

The normal component of which quantity is always discontinuous at the boundary?

• A. Electric Field (E)
• B. Electric Displacement Field (D)
• C. Magnetic Field (B)
• D. Magnetic Field Intensity (H)

Answer 1

Answer: (D)

Magnetic Field Intensity (H)

Answer 2

The normal component of the magnetic field ($\vec{B}$) is always continuous across a boundary ($B_{1n} = B_{2n}$) due to the absence of magnetic monopoles. The normal component of the electric displacement field ($\vec{D}$) is discontinuous only if there is a surface charge density ($\sigma_s \neq 0$). The normal component of the electric field ($\vec{E}$) is discontinuous if there is a surface charge density or if the permittivities of the media are different. The normal component of the magnetic field intensity ($\vec{H}$) is related to $\vec{B}$ by $\vec{B} = \mu \vec{H}$. Since $B_{1n} = B_{2n}$, it follows that $\mu_1 H_{1n} = \mu_2 H_{2n}$. Therefore, $H_{1n} = (\mu_2/\mu_1) H_{2n}$. The normal component of $\vec{H}$ is continuous only if $\mu_1 = \mu_2$. At a boundary between different materials, $\mu_1 \neq \mu_2$, making the normal component of $\vec{H}$ discontinuous. While not "always" discontinuous in the most literal sense (e.g., if the media are identical), it is the quantity whose normal component is generally discontinuous at a material boundary.