Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Time varying electric field produces magnetic fields. Reason (R): Time varying magnetic field produces electric fields. In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Maxwell's equations imply: \[ \text{Changing } E \Rightarrow H \] and \[ \text{Changing } H \Rightarrow E \] These interactions enable electromagnetic wave propagation.

Answer 1

The Correct Option is B

Concept: Electromagnetic field theory is governed by Maxwell’s equations. Two important Maxwell equations are: \[ \nabla \times \vec{E}=-\frac{\partial \vec{B}}{\partial t} \] and \[ \nabla \times \vec{H}=\vec{J}+\frac{\partial \vec{D}}{\partial t} \] These imply:
• Time varying magnetic field produces electric field.
• Time varying electric field produces magnetic field.

Step 1: Analyze Assertion (A). Assertion says: Time varying electric field produces magnetic fields. This is correct according to Maxwell’s displacement current concept: \[ \nabla \times \vec{H}=\frac{\partial \vec{D}}{\partial t} \] Thus changing electric field generates magnetic field. Hence: \[ (A)\text{ is correct} \]

Step 2: Analyze Reason (R). Reason states: Time varying magnetic field produces electric fields. This is also correct according to Faraday’s law: \[ \nabla \times \vec{E}=-\frac{\partial \vec{B}}{\partial t} \] Hence: \[ (R)\text{ is correct} \]

Step 3: Check explanatory relationship. Although both statements are true:
• Reason does not directly explain Assertion.
• They are two independent Maxwell equations. Therefore:
• Both are correct.
• But Reason is not the correct explanation of Assertion.

Step 4: Write the final answer. Hence, the correct option is: \[ \boxed{(B)\ \text{Both (A) and (R) are correct but (R) is not the correct explanation of (A)}} \]