Question

Which of the following statements are correct regarding the electric and magnetic fields at any surface of discontinuity ?
• [A.] The tangential component of \(E\) is continuous at the surface
• [B.] The tangential component of \(H\) is continuous across a surface except at the surface of a perfect conductor
• [C.] The tangential component of \(B\) is continuous at the surface of discontinuity
• [D.] The normal component of \(D\) is continuous if there is no surface charge density Choose the correct answer from the options given below :

• A. A, B, D only
• B. A, B, C only
• C. B, C, D only
• D. A, C, D only

Hint:

Important electromagnetic boundary conditions:
• Tangential \(E\) is continuous
• Normal \(B\) is continuous
• Normal \(D\) changes with surface charge density
• Tangential \(H\) changes with surface current density

Answer 1

The Correct Option is A

Concept: Electromagnetic boundary conditions are derived from Maxwell’s equations. At the interface between two media:
• Tangential and normal components of field vectors obey specific continuity relations. Important boundary conditions are: :contentReference[oaicite:2]{index=2} and :contentReference[oaicite:3]{index=3}

Step 1: Analyze statement A. Statement A: \[ \text{Tangential component of }E\text{ is continuous} \] From boundary conditions: \[ E_{t1}=E_{t2} \] Hence: \[ A \text{ is correct} \]

Step 2: Analyze statement B. Statement B: \[ \text{Tangential component of }H\text{ is continuous except at perfect conductor} \] This is correct because:
• Surface current density may create discontinuity.
• Perfect conductors alter tangential magnetic field behavior. Hence: \[ B \text{ is correct} \]

Step 3: Analyze statement C. Statement C: \[ \text{Tangential component of }B\text{ is continuous} \] This statement is not generally used as a standard boundary condition. Actually:
• Normal component of \(B\) is continuous. Therefore: \[ C \text{ is incorrect} \]

Step 4: Analyze statement D. Statement D: \[ \text{Normal component of }D\text{ is continuous if surface charge density is zero} \] From boundary condition: \[ D_{n2}-D_{n1}=\rho_s \] If: \[ \rho_s=0 \] then: \[ D_{n1}=D_{n2} \] Hence: \[ D \text{ is correct} \]

Step 5: Write final answer. Correct statements are: \[ A,\ B,\ D \] Thus the correct option is: \[ \boxed{(A)} \]