Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Electromagnetic Waves

NTA Abhyas 2020 · Physics · Electromagnetic Waves

The magnetic field of a plane electromagnetic wave is given by → B...

The magnetic field of a plane electromagnetic wave is given by \overset{→}{B} = {B}_{0}\overset{^}{i} \left[\cos \left(kz - \omegat\right)\right] + {B}_{1}\overset{^}{j}\cos \left(kz + \omegat\right), where B0=3×10–5T{B}_{0} = 3 \times {10}^{– 5}T and B1=2×10–6T{B}_{1} = 2 \times {10}^{– 6}T. The RMS value of the force experienced by a stationary charge Q=10–4CQ = {10}^{– 4}C at z=0isclosesttoz = 0 is closest to

Options

  1. A0.1N0.1N
  2. B0.9N0.9N
  3. C3×10–2N3 \times {10}^{– 2}N
  4. D0.6N0.6N

Correct answer

D. 0.6N0.6N

Step-by-step solution

\overset{→}{B} = {B}_{0}\overset{^}{i} \left[\cos \left(kz - \omegat\right)\right] + {B}_{1}\overset{^}{j}\cos \left(kz + \omegat\right)
B0=3×10−5TB1=2×10−6T{B}_{0} = 3 \times {10}^{- 5}T{B}_{1} = 2 \times {10}^{- 6}T
Electric filed associated with it is,
\overset{→}{E} = - {B}_{0}c\overset{^}{j}\cos \left(kz - \omegat\right) - {B}_{1}c\overset{^}{i}\cos \left(kz + \omegat\right)
Here, c is speed of light in vacuum.
At z=0,z = 0,
Frms=(QB0c)2+(QB1c)22{F}_{\text{rms}} = \sqrt{\dfrac{{\left(Q{B}_{0}c\right)}^{2} + {\left(Q{B}_{1}c\right)}^{2}}{2}}
Here cc is speed of light in vacuum.
=(10−4×3×10−5×3×108)2+(10−4×2×10−6×3×108)22= \sqrt{\dfrac{{ \left({10}^{- 4} \times 3 \times {10}^{- 5} \times 3 \times {10}^{8}\right)}^{2} + { \left({10}^{- 4} \times 2 \times {10}^{- 6} \times 3 \times {10}^{8}\right)}^{2}}{2}}
=0.81+0.00362== \sqrt{\dfrac{0.81 + 0.0036}{2}} =0.6N
Practice Electromagnetic Waves on Quantrex Academy →

More from Electromagnetic Waves

The electric field associated with an electromagnetic wave travelling in vacuum is given… JEE Advanced 2026A monochromatic source of light operating at 15 kW emits 2.5× 10^ 22 photons/s. The… JEE Main 2026For an electromagnetic wave propagating through vacuum, k , E and ω represent propagation… JEE Main 2026A point light source emits E.M. waves in free space. A detector, placed at a distance of… JEE Main 2026A displacement current of 4.0 A can be set up in the space between two parallel plates of… JEE Main 2026A magnetic field vector in an electromagnetic wave is represented by B =B_0 (2π vt-(2π… JEE Main 2026An electromagnetic wave travels in free space along the x -direction. At a particular… JEE Main 2026An electromagnetic wave travelling in x -direction is described by field equation E_y =… JEE Main 2026 Full Electromagnetic Waves list All NTA Abhyas JEE Main PYQs