Match List I with List II: Gauss’s Law in Electrostatics [2023]

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Solution

Q.
Match List I with List II: [2023]

List I List II

A. Gauss’s Law in Electrostatics I. $\oint \vec{E} \cdot d \vec{l} = - \frac{d ϕ_{B}}{d t}$

B. Faraday’s Law II. $\oint \vec{B} \cdot d \vec{A} = 0$

C. Gauss’s Law in Magnetism III. $\oint \vec{B} \cdot d \vec{l} = μ_{0} i_{c} + μ_{0} ε_{0} \frac{d ϕ_{E}}{d t}$

D. Ampere-Maxwell Law IV. $\oint \vec{E} \cdot d \vec{S} = \frac{q}{ε_{0}}$

Choose the correct answer from the options given below:

1 A-I, B-II, C-III, D-IV

2 A-IV, B-I, C-II, D-III

3 A-III, B-IV, C-I, D-II

4 A-II, B-III, C-IV, D-I

Ans.
(2)

Gauss's law of electrostatics

$ϕ = \oint \vec{E} \cdot d \vec{s} = \frac{q}{ε_{0}}$

Faraday's law $\oint \vec{E} \cdot d \vec{l} = \frac{- d ϕ_{B}}{d t}$

Gauss's law of magnetism $\oint \vec{B} \cdot d \vec{A} = 0$

Ampere's Maxwell law

$\oint \vec{B} \cdot d \vec{l} = μ_{0} i_{C} + μ_{0} ε_{0} \frac{d ϕ_{E}}{d t}$

Where $i_{C}$ : Conduction current

$ε_{0} \frac{d ϕ_{E}}{d t}$ : Displacement current

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