Topic: Electromagnetics
A boundary separates two magnetic materials of permeability $\mu_{1}$ and $\mu_{2}$. The magnetic field vector in $\mu_{1}$ is $H_{1}$ with a normal component $H_{n_{1}}$ and tangential component $H_{t_{1}}$ while that in $\mu_{2}$ is $H_{2}$ with a normal component $H_{n_{2}}$ and tangential component $H_{t_{2}}$ Then the derived condition would be
- A. $H_{1}=H_{2}$ and $H_{t_{1}}=H_{t_{2}}$
- B. $H_{t_{1}}=H_{t_{2}}$ and $\mu_{1}H_{n_{1}}=\mu_{2}H_{n_{2}}$
- C. $H_{1}=H_{2}$ and $\mu_{1}H_{n_{1}}=\mu_{2}H_{n_{2}}$
- D. $H_{1}=H_{2}$, $H_{t_{1}}=H_{t_{2}}$ and $\mu_{1}H_{n_{1}}=\mu_{2}H_{n_{2}}$
Answer: B. $H_{t_{1}}=H_{t_{2}}$ and $\mu_{1}H_{n_{1}}=\mu_{2}H_{n_{2}}$
Explanation: At the boundary between two magnetic media, assuming no surface current density, the tangential component of the magnetic field intensity ($H$) is continuous: $H_{t_1} = H_{t_2}$. The normal component of the magnetic flux density ($B$) is always continuous: $B_{n_1} = B_{n_2}$. Since $B = \mu H$, this gives $\mu_1 H_{n_1} = \mu_2 H_{n_2}$.