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Electromagnetic Waves question

2023 · 25 Jan · Shift 2 · Q53
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  5. /2023 · 25 Jan · Shift 2 · Q53

Electromagnetic Waves question

2023 · 25 Jan · Shift 2 · Q53

JEE MainPhysicsElectromagnetic WavesMCQ+4 / −1

Match List I with List II

List I List II
A. Gauss's Law in Electrostatics I. ∮E→ . dl→=−dϕBdt\oint {\overrightarrow E \,.\,d\overrightarrow l = - {{d{\phi _B}} \over {dt}}}∮E.dl=−dtdϕB​​
B. Faraday's Law II. ∮B→ . dA→=0\oint {\overrightarrow B \,.\,d\overrightarrow A = 0}∮B.dA=0
C. Gauss's Law in Magnetism III. ∮B→ . dl→=μ0ic+μ0∈0dϕEdt\oint {\overrightarrow B \,.\,d\overrightarrow l = {\mu _0}{i_c} + {\mu _0}{ \in _0}{{d{\phi _E}} \over {dt}}}∮B.dl=μ0​ic​+μ0​∈0​dtdϕE​​
D. Ampere-Maxwell Law IV. ∮E→ . ds→=q∈0\oint {\overrightarrow E \,.\,d\overrightarrow s = {q \over {{ \in _0}}}}∮E.ds=∈0​q​

Choose the correct answer from the options given below :

  1. A
    A-I, B-II, C-III, D-IV
  2. B
    A-III, B-IV, C-I, D-II
  3. C
    A-IV, B-I, C-II, D-III
  4. D
    A-II, B-III, C-IV, D-I
View written solutionFree

Correct answer: C

  1. We match each law in List I with its corresponding mathematical form in List II.
  1. A. Gauss's Law in Electrostatics

Gauss's law in electrostatics is

∮E⃗⋅dS⃗=qε0\oint \vec E \cdot d\vec S = \frac{q}{\varepsilon_0}∮E⋅dS=ε0​q​

This corresponds to IV.

So, A→IVA \to IVA→IV

  1. B. Faraday's Law

Faraday's law of electromagnetic induction is

∮E⃗⋅dl⃗=−dϕBdt\oint \vec E \cdot d\vec l = -\frac{d\phi_B}{dt}∮E⋅dl=−dtdϕB​​

This corresponds to I.

So, B→IB \to IB→I

  1. C. Gauss's Law in Magnetism

Gauss's law in magnetism states that net magnetic flux through a closed surface is zero:

∮B⃗⋅dA⃗=0\oint \vec B \cdot d\vec A = 0∮B⋅dA=0

This corresponds to II.

So, C→IIC \to IIC→II

  1. D. Ampere-Maxwell Law

Ampere-Maxwell law is

∮B⃗⋅dl⃗=μ0ic+μ0ε0dϕEdt\oint \vec B \cdot d\vec l = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt}∮B⋅dl=μ0​ic​+μ0​ε0​dtdϕE​​

This corresponds to III.

So, D→IIID \to IIID→III

  1. Therefore the full matching is:
A−IV,  B−I,  C−II,  D−IIIA-IV,\; B-I,\; C-II,\; D-IIIA−IV,B−I,C−II,D−III

This matches Option C.

  1. Comparison with stored correct answer

Stored correct answer = C

Our derived answer = C

Hence, they agree.

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