Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainPhysicsElectromagnetic Waves

The electric field of a plane electromagnetic wave propagating in free space is given by E = E₀ (kz - t) . The instantaneous magnetic energy density U_B associated with this wave is ( c is the speed of light in free space, ₀ is the permeability of free space):

Options

  1. AE₀^2 2 ₀ ^2(kz - t)
  2. BE₀^2 4 ₀ c^2 ^2(kz - t)
  3. C₀ E₀^2 2 c^2 ^2(kz - t)
  4. DE₀^2 2 ₀ c^2 ^2(kz - t)

Correct answer

D. E₀^2 2 ₀ c^2 ^2(kz - t)

Step-by-step solution

The instantaneous magnetic energy density is given by U_B = B^2 2 ₀ . For an electromagnetic wave, the magnitudes of the electric and magnetic fields are related by B = E c . Substituting this into the energy density formula gives: U_B = 1 2 ₀ ( E c )^2 = E^2 2 ₀ c^2 Given E = E₀ (kz - t) , we substitute this to find the instantaneous magnetic energy density: U_B = E₀^2 2 ₀ c^2 ^2(kz - t) Answer: E₀^2 2 ₀ c^2 ^2(kz - t)

Practice Electromagnetic Waves on Quantrex Academy →

More from Electromagnetic Waves

The electric field associated with an electromagnetic wave travelling in vacuum is given by E₀ (3y + 4z + t) , i , where is the angular frequency. All quantities are in SI units. T 2026A monochromatic source of light operating at 15 kW emits 2.5 10²² photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ___ 2026For an electromagnetic wave propagating through vacuum, k , E and represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated wi 2026A point light source emits E.M. waves in free space. A detector, placed at a distance of L m, measures the intensity as I_o . The detector is now shifted to another location on the 2026A displacement current of 4.0 A can be set up in the space between two parallel plates of 6 F capacitor. The rate of change of potential difference across the plates of the capacit 2026A magnetic field vector in an electromagnetic wave is represented by B =B₀ (2 vt- 2 x ) j . Its associated electric field vector is ______. 2026An electromagnetic wave travels in free space along the x -direction. At a particular point in space and time, B = 2 10⁻⁷ j T is associated with this wave. The value of correspondi 2026An electromagnetic wave travelling in x -direction is described by field equation E_y = 300 (t - x c ) . If the electron is restricted to move in y -direction only with speed of 1. 2026 Full Electromagnetic Waves list All JEE Main PYQs