KCET · Physics · Electromagnetic Waves
Match the following Maxwell's equations:
(The symbols used here have their usual meanings)
| List-I | List-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) | \(\oint \vec{E} \cdot d\vec{l} = -\dfrac{d\phi_B}{dt}\) |
- A a - i, b - iii, c - iv, d – ii
- B a - ii, b - iii, c - i, d – iv
- C a - i, b - ii, c - iii, d – iv
- D a - ii, b - iii, c - iv, d – i
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
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
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