Electromagnetic Waves Previous Year Questions — JEE Main Physics
31 past-year Electromagnetic Waves questions from JEE Main (Physics) — page 4.
Q40 (2024)
Match List I with List II:
<div style="overflow-x: auto; margin: 1rem 0;"><div class="rankbit-table-container"><table class="rankbit-table"><thead><tr><th style="border: 1px solid #888; padding: 8px;">List I</th><th style="border: 1px solid #888; padding: 8px;">List II</th></tr></thead><tbody><tr><td style="border: 1px solid #888; padding: 8px;">A. $\oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt}$</td><td style="border: 1px solid #888; padding: 8px;">I. Gauss' law for electricity</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">B. $\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}$</td><td style="border: 1px solid #888; padding: 8px;">II. Gauss' law for magnetism</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">C. $\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}$</td><td style="border: 1px solid #888; padding: 8px;">III. Faraday law</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">D. $\oint \vec{B} \cdot d\vec{A} = 0$</td><td style="border: 1px solid #888; padding: 8px;">IV. Ampere - Maxwell law</td></tr></tbody></table></div></div>
Choose the correct answer from the options given below:
- A-IV, B-I, C-III, D-II
- A-II, B-III, C-I, D-IV
- A-IV, B-III, C-I, D-II
- A-I, B-II, C-III, D-IV
### Core Logic
Let's review the fundamental Maxwell's equations:
1. **Ampere - Maxwell Law** relates the magnetic path integral to conduction current and displacement current:
$$\oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt} \implies \text{A - IV}$$
2. **Faraday's Law of Induction** states that changing magnetic flux induces an electromotive force (EMF):
$$\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt} \implies \text{B - III}$$
3. **Gauss's Law for Electricity** relates net electric flux to enclosed charge:
$$\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0} \implies \text{C - I}$$
4. **Gauss's Law for Magnetism** states that magnetic monopoles do not exist:
$$\oint \vec{B} \cdot d\vec{A} = 0 \implies \text{D - II}$$
### Step 1: Match Evaluation
The match configurations are:
* A $\rightarrow$ IV
* B $\rightarrow$ III
* C $\rightarrow$ I
* D $\rightarrow$ II
This perfectly corresponds to Option (3).
### Pattern Recognition
Understand the integral geometries: Path integrals (line integrals $\oint \cdot d\vec{l}$) correspond to circulating fields (induction laws like Ampere/Faraday). Surface integrals (flux integrals $\oint \cdot d\vec{A}$) correspond to bounded charge states (Gauss laws).
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Electromagnetic Waves
Class 12 Physics: Electrostatics
Class 12 Physics: Magnetism and Matter
Q40 (2024)
If the total energy transferred to a surface in time $t$ is $6.48 \times 10^{5} \mathrm{~J}$, then the magnitude of the total momentum delivered to this surface for complete absorption will be:
- $2.46 \times 10^{-3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
- $2.16 \times 10^{-3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
- $1.58 \times 10^{-3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
- $4.32 \times 10^{-3} \mathrm{~kg} \mathrm{~m} / \mathrm{s}$
### Related Formula
$$p = \frac{U}{c}$$
### Core Logic
For an electromagnetic wave incident on a surface that is completely absorbed, the total momentum transferred is equal to the total energy transferred divided by the speed of light in vacuum ($c$).
### Step 1: Calculate Momentum
Given total energy $E = 6.48 \times 10^5 \mathrm{~J}$.
Speed of light $c = 3 \times 10^8 \mathrm{~m/s}$.
$$p = \frac{E}{c} = \frac{6.48 \times 10^5}{3 \times 10^8}$$
$$p = 2.16 \times 10^{-3} \mathrm{~kg~m/s}$$
### Pattern Recognition
Always check for "complete absorption" versus "perfect reflection". For complete absorption, $p = E/c$. For perfect reflection, $p = 2E/c$.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Electromagnetic Waves
Q49 (2024)
Match List I with List II:
<div style="overflow-x: auto; margin: 1rem 0;"><table style="width: 100%; border-collapse: collapse; text-align: left; font-size: 14px;"><thead><tr><th style="border: 1px solid #888; padding: 8px;">List-I</th><th style="border: 1px solid #888; padding: 8px;">List-II</th></tr></thead><tbody><tr><td style="border: 1px solid #888; padding: 8px;">A. Gauss's law of magnetostatics</td><td style="border: 1px solid #888; padding: 8px;">I. $\oint \vec{E} \cdot \mathrm{d}\vec{a} = \frac{1}{\varepsilon_0} \int \rho \mathrm{d}V$</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">B. Faraday's law of electro magnetic induction</td><td style="border: 1px solid #888; padding: 8px;">II. $\oint \vec{B} \cdot \mathrm{d}\vec{a} = 0$</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">C. Ampere's law</td><td style="border: 1px solid #888; padding: 8px;">III. $\oint \vec{E} \cdot \mathrm{d}\vec{l} = -\frac{\mathrm{d}}{\mathrm{d}t}\int \vec{B} \cdot \mathrm{d}\vec{a}$</td></tr><tr><td style="border: 1px solid #888; padding: 8px;">D. Gauss's law of electrostatics</td><td style="border: 1px solid #888; padding: 8px;">IV. $\oint \vec{B} \cdot \mathrm{d}\vec{l} = \mu_0 I$</td></tr></tbody></table></div>
Choose the correct answer from the options given below:
- $\text{A-I, B-III, C-IV, D-II}$
- $\text{A-III, B-IV, C-I, D-II}$
- $\text{A-IV, B-II, C-III, D-I}$
- $\text{A-II, B-III, C-IV, D-I}$
### Core Logic
Match each law with its corresponding mathematical expression (Maxwell's equations).
(A) Gauss's law of magnetostatics: The net magnetic flux through any closed surface is zero. $\oint \vec{B} \cdot \mathrm{d}\vec{a} = 0$ (Matches II).
(B) Faraday's law of electromagnetic induction: The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux. $\oint \vec{E} \cdot \mathrm{d}\vec{l} = -\frac{\mathrm{d}}{\mathrm{d}t} \int \vec{B} \cdot \mathrm{d}\vec{a}$ (Matches III).
(C) Ampere's law: The line integral of the magnetic field around a closed loop is proportional to the electric current passing through the loop. $\oint \vec{B} \cdot \mathrm{d}\vec{l} = \mu_0 I$ (Matches IV).
(D) Gauss's law of electrostatics: The electric flux through any closed surface is proportional to the enclosed electric charge. $\oint \vec{E} \cdot \mathrm{d}\vec{a} = \frac{1}{\varepsilon_0} \int \rho \mathrm{d}V$ (Matches I).
### Step 1: Final Match
A $\rightarrow$ II
B $\rightarrow$ III
C $\rightarrow$ IV
D $\rightarrow$ I
This matches option (4).
### Pattern Recognition
These are the fundamental Maxwell equations in integral form. Memorizing their direct mappings guarantees quick marks.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Electromagnetic Waves
Class 12 Physics: Electromagnetic Induction
Q38 (2024)
The electric field of an electromagnetic wave in free space is represented as $\vec{E} = E_0\cos (\omega t - kz)\hat{i}$ The corresponding magnetic induction vector will be:
- $\vec{B} = E_0C\cos (\omega t - kz)\hat{j}$
- $\vec{B} = \frac{E_0}{C} \cos (\omega t - kz) \hat{j}$
- $\vec{B} = E_0C\cos (\omega t + kz)\hat{j}$
- $\vec{B} = \frac{E_0}{C}\cos (\omega t + kz)\hat{j}$
### Related Formula
$$B_0 = \frac{E_0}{C}$$
$$\hat{C} = \hat{E} \times \hat{B}$$
### Core Logic
In an electromagnetic wave in free space, the magnitudes of the electric and magnetic fields are related by $E_0 = c B_0$. Thus, $B_0 = E_0 / C$.
The direction of wave propagation is given by the cross product of the electric field and magnetic field vectors: $\hat{C} = \hat{E} \times \hat{B}$.
### Step 1: Determine Wave Direction and Magnetic Field Direction
Given the phase term $(\omega t - kz)$, the wave propagates in the $+z$ direction, so $\hat{C} = \hat{k}$.
The electric field oscillates in the $+x$ direction, so $\hat{E} = \hat{i}$.
We know:
$$\hat{k} = \hat{i} \times \hat{B}$$
Since $\hat{i} \times \hat{j} = \hat{k}$, the magnetic field must oscillate in the $+y$ direction ($\hat{j}$).
### Step 2: Construct Final Vector
The full magnetic field vector shares the same phase and applies the above amplitude and direction:
$$\vec{B} = \frac{E_0}{C} \cos(\omega t - kz) \hat{j}$$
### Pattern Recognition
Phase remains identical. Amplitude scales by $1/c$. Direction satisfies the right-hand triad $(\vec{E}, \vec{B}, \vec{v})$ where $\vec{v} = \vec{E} \times \vec{B}$.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Electromagnetic Waves
Q40 (2024)
Given below are two statements:
Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields.
Statement II: When electromagnetic waves strike a surface, a pressure is exerted on the surface.
In the light of the above statements, choose the most appropriate answer from the options given below:
- Statement I is incorrect but Statement II is correct
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
### Related Formula
$$\rho_E = \frac{1}{2}\varepsilon_0 E_{rms}^2$$
$$\rho_B = \frac{B_{rms}^2}{2\mu_0}$$
$$p_r = \frac{I}{c}$$ (radiation pressure for completely absorbing surface)
### Core Logic
Statement I: In an EM wave, energy is stored in both the electric and magnetic fields. The energy densities are equal: $U_E = U_B$ because $E = cB$ and $c^2 = \frac{1}{\mu_0 \epsilon_0}$. This is a correct fact.
Statement II: Electromagnetic waves carry momentum ($p = U/c$). When they strike a surface, they transfer this momentum, creating radiation pressure. This is also a correct fact.
### Step 1: Final Evaluation
Since both facts are universally true theoretical properties of EM waves, both statements are correct.
### Pattern Recognition
Standard NCERT theory. Energy density is strictly symmetric 50-50 between E and B. Momentum transfer $\to$ pressure is the definitive signature of the particle-like nature (photons) of EM waves.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Electromagnetic Waves
