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JEE Main 202313 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
13 April
Shift
Morning Shift
Subject
Physics
Chapter
Electromagnetic Waves

JEE Main 2023 · 13 April · Morning Shift · Physics · Electromagnetic Waves

Which of the following Maxwell’s equation is valid for time...

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

Options

  1. A∮B→⋅dl→=μ0I∮ \overset{\to}{B} \cdot \overset{\to}{dl} = {\mu}_{0}I
  2. B∮E→⋅dl→=0∮ \overset{\to}{E} \cdot \overset{\to}{dl} = 0
  3. C∮D→⋅dA→=Q∮ \overset{\to}{D} \cdot \overset{\to}{dA} = Q
  4. D∮E→⋅dl→=−∂ϕB∂t∮ \overset{\to}{E} \cdot d\overset{\to}{l} = - \dfrac{∂ {ϕ}_{B}}{∂ t}

Correct answer

D. ∮E→⋅dl→=−∂ϕB∂t∮ \overset{\to}{E} \cdot d\overset{\to}{l} = - \dfrac{∂ {ϕ}_{B}}{∂ t}

Step-by-step solution

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:

∮E→⋅dA→=qε0...(1)∮B⇀⋅dA⇀=0...(2)∮E⇀⋅dl⇀=−∂ϕB∂t...(3)∮B⇀⋅dl⇀=μ0I...(4)∮ \overset{\to}{E} \cdot d\overset{\to}{A} = \dfrac{q}{{ε}_{0}} . . . \left(1\right) ∮ \overset{⇀}{B} \cdot d\overset{⇀}{A} = 0 . . . \left(2\right) ∮ \overset{⇀}{E} \cdot d\overset{⇀}{l} = - \dfrac{∂ {ϕ}_{B}}{∂ t} . . . \left(3\right) ∮ \overset{⇀}{B} \cdot d\overset{⇀}{l} = {\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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