Electromagnetic Waves

JEE Main level, single correct, medium

46 of 165

Question 46 of 165

Which of the following Maxwell’s equation is valid for time varying conditions but not valid for static conditions:

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Answer: (D) ∮E⃗⋅dl⃗=−∂ϕB∂t\oint \vec{E}\cdot d\vec{l}=-\dfrac{\partial {\phi }_{B}}{\partial t}

Maxwell’s four equations describe the electric and magnetic fields arising from distributions of electric charges and currents, and how those fields change in time.
The equations are as follows:
∮E⃗⋅dA⃗=qϵ0...(1)∮B⇀⋅dA⇀=0...(2)∮E⇀⋅dl⇀=−∂ϕB∂t...(3)∮B⇀⋅dl⇀=μ0I...(4)\oint \vec{E}\cdot d\vec{A}=\dfrac{q}{{\epsilon }_{0}}...\left(1\right) \oint B^{⇀}\cdot dA^{⇀}=0...\left(2\right) \oint E^{⇀}\cdot dl^{⇀}=-\dfrac{\partial {\phi }_{B}}{\partial t}...\left(3\right) \oint B^{⇀}\cdot dl^{⇀}={\mu }_{0}I...\left(4\right)
From the above set of equations, it is clear that only the third equation is valid for time varying field.
Hence, this is the correct option.

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