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KCET · Physics · Electromagnetic Waves

Match the following Maxwell's equations:
(The symbols used here have their usual meanings)
List-IList-II
(a)Gauss' law for electrostatics(i)\(\oint \vec{E} \cdot d\vec{A} = \dfrac{Q}{\varepsilon_0}\)
(b)Gauss' law for magnetism(ii)\(\oint \vec{B} \cdot d\vec{l} = \mu_0 \left[i_c + \varepsilon_0 \dfrac{d\phi_E}{dt}\right]\)
(c)Faraday's law(iii)\(\oint \vec{B} \cdot d\vec{A} = 0\)
(d)Ampere-Maxwell's law(iv)\(\oint \vec{E} \cdot d\vec{l} = -\dfrac{d\phi_B}{dt}\)

  1. A a - i, b - iii, c - iv, d – ii
  2. B a - ii, b - iii, c - i, d – iv
  3. C a - i, b - ii, c - iii, d – iv
  4. D a - ii, b - iii, c - iv, d – i
Verified Solution

Answer & Solution

Correct Answer

(A) a - i, b - iii, c - iv, d – ii

Step-by-step Solution

Detailed explanation

Gauss' law for electrostatics relates the electric flux through a closed surface to the enclosed charge: \(\oint \vec{E} \cdot d\vec{A} = \dfrac{Q}{\varepsilon_0}\).

Gauss' law for magnetism states that the net magnetic flux through any closed surface is zero: \(\oint \vec{B} \cdot d\vec{A} = 0\).

Faraday's law of induction relates the induced electric field along a closed loop to the rate of change of magnetic flux through the loop: \(\oint \vec{E} \cdot d\vec{l} = -\dfrac{d\phi_B}{dt}\).

Ampere-Maxwell's law relates the magnetic field along a closed loop to the conduction current and the rate of change of electric flux (displacement current): \(\oint \vec{B} \cdot d\vec{l} = \mu_0 \left[i_c + \varepsilon_0 \dfrac{d\phi_E}{dt}\right]\).

Thus, the correct matching is a - i, b - iii, c - iv, d - ii.

Answer: a - i, b - iii, c - iv, d – ii