JEE Mains · Physics · STD 12 - Electromagnetic waves
- JEE Mains 2026
- Medium
- MCQ
An electromagnetic wave travelling in \(x\)-direction is described by field equation \(E_y = 300\sin\omega\left(t - \dfrac{x}{c}\right)\). If the electron is restricted to move in \(y\)-direction only with speed of \(1.5 \times 10^6\) m/s then ratio of maximum electric and magnetic forces acting on the electron is _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(200\)
Step-by-step Solution
Detailed explanation
The maximum electric force acting on the electron is \(F_e = eE_0\).
The maximum magnetic force acting on the electron is \(F_m = evB_0\), where \(v\) is the speed of the electron and \(B_0\) is the maximum magnetic field.
The ratio of the maximum electric force to the maximum magnetic force is given by \(\dfrac{F_e}{F_m} = \dfrac{eE_0}{evB_0} = \dfrac{E_0}{vB_0}\).
For an electromagnetic wave, the ratio of the amplitudes of the electric and magnetic fields is \(\dfrac{E_0}{B_0} = c\), where \(c\) is the speed of light in vacuum.
Substituting this into the ratio of forces yields \(\dfrac{F_e}{F_m} = \dfrac{c}{v}\).
Given \(c = 3 \times 10^8\) m/s and \(v = 1.5 \times 10^6\) m/s, we get \(\dfrac{F_e}{F_m} = \dfrac{3 \times 10^8}{1.5 \times 10^6} = 200\).
Answer: \(200\)
The maximum magnetic force acting on the electron is \(F_m = evB_0\), where \(v\) is the speed of the electron and \(B_0\) is the maximum magnetic field.
The ratio of the maximum electric force to the maximum magnetic force is given by \(\dfrac{F_e}{F_m} = \dfrac{eE_0}{evB_0} = \dfrac{E_0}{vB_0}\).
For an electromagnetic wave, the ratio of the amplitudes of the electric and magnetic fields is \(\dfrac{E_0}{B_0} = c\), where \(c\) is the speed of light in vacuum.
Substituting this into the ratio of forces yields \(\dfrac{F_e}{F_m} = \dfrac{c}{v}\).
Given \(c = 3 \times 10^8\) m/s and \(v = 1.5 \times 10^6\) m/s, we get \(\dfrac{F_e}{F_m} = \dfrac{3 \times 10^8}{1.5 \times 10^6} = 200\).
Answer: \(200\)
More questions from Physics
- The magnetic field of an electromagnetic wave is given by \(\vec B = 1.6 \times {10^{ - 6}}\,\cos \,\left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {2\hat i + \hat j} \right)\frac{{Wb}}{{{m^2}}}\) The associated electric field will beJEE Mains 2019 Medium
- For a series \(LCR\) circuit with \({R}=100\,\ \Omega, {L}=0.5\, {mH}\) and \({C}=0.1\, {pF}\) connected across \(220 \,{V}-50\, {Hz}\) \(AC\) supply, the phase angle between current and supplied voltage and the nature of the circuit is :JEE Mains 2021 Medium
- If \(\overrightarrow{ P }=3 \hat{ i }+\sqrt{3} \hat{ j }+2 \hat{ k }\) and \(\overrightarrow{ Q }=4 \hat{ i }+\sqrt{3} \hat{ j }+2.5 \hat{ k }\) then, The unit vector in the direction of \(\overrightarrow{ P } \times \overrightarrow{ Q }\) is \(\frac{1}{x}(\sqrt{3} \hat{i}+\hat{j}-2 \sqrt{3} \hat{k})\). The value of \(x\) isJEE Mains 2023 Medium
- For ac circuit shown in figure, \(\mathrm{R}=100 \mathrm{k} \Omega\) and \(\mathrm{C}=100 \mathrm{pF}\) and the phase difference between \(\mathrm{V}_{\text {in }}\) and \(\left(V_B-V_A\right)\) is \(90^{\circ}\). The input signal frequency is \(10^x \mathrm{rad} / \mathrm{sec}\), where ' x ' is ______.
JEE Mains 2025 Hard - Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for \(V =5 \sin (100 t )\). The values of L and \(R\) are shown in the figure. The capacitance of the capacitor \(( C )\) used is ___________ \(\mu F\).
JEE Mains 2026 Hard - The width of one of the two slits in a Young's double slit experiment is \(4\) times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is _______.JEE Mains 2024 Hard
More PYQs from JEE Mains
- Two satellites \(A\) and \(B\) of masses \(200\, kg\) and \(400\, kg\) are revolving round the earth at height of \(600\, km\) and \(1600\, km\) respectively. If \(T _{ A }\) and \(T _{ B }\) are the time periods of \(A\) and \(B\) respectively then the value of \(T _{ B }- T _{ A }\) [Given : radius of earth \(=6400\, km\), mass of earth \(=6 \times 10^{24}\, kg\) ]
JEE Mains 2021 Hard - If the capacitance of a nanocapacitor is measured in terms of a unit \(u\) made by combining the electric charge \(e,\) Bohr radius \(a_0,\) Planck's constant \(h\) and speed of light \(c\) thenJEE Mains 2015 Hard
- There are two long co -axial solenoids of same length \(l.\) The inner and outer coils have radii \(r_1\) and \(r_2\) and number of turns per unit length \(n_1\) and \(n_2\) respectively. The ratio of mutual inductance to the self -inductance of the inner -coil isJEE Mains 2019 Hard
- The relative error in the determination of the surface area of a sphere is \(\alpha \). Then the relative error in the determination of its volume isJEE Mains 2018 Hard