Exams › JEE Advanced › Physics

The electric field of an electromagnetic wave in vacuum is given by E = (3.1 N/C) cos[(1.8 rad/m) y + (5.4 × 10⁸ rad/s) t] i. (a) In which direction does the wave travel? (b) Find the wavelength λ. (c) Find the frequency ν. (d) Find the amplitude of the magnetic field B0. (e) Write the expression for the magnetic field of the wave.

1. Propagation along -y; λ = 3.49 m; ν = 8.6 × 10⁷ Hz; B0 = 1.03 × 10⁻⁸ T; B = (1.03 × 10⁻⁸ T) cos[(1.8 rad/m) y + (5.4 × 10⁸ rad/s) t] k
2. Propagation along +y; λ = 1.75 m; ν = 4.3 × 10⁷ Hz; B0 = 2.06 × 10⁻⁸ T; B = (2.06 × 10⁻⁸ T) cos[...] k
3. Propagation along +x; λ = 3.49 m; ν = 8.6 × 10⁷ Hz; B0 = 1.03 × 10⁻⁸ T; B = (1.03 × 10⁻⁸ T) cos[...] j
4. Propagation along -z; λ = 3.49 m; ν = 1.72 × 10⁸ Hz; B0 = 0.52 × 10⁻⁸ T; B = (0.52 × 10⁻⁸ T) cos[...] k

Correct answer: Propagation along -y; λ = 3.49 m; ν = 8.6 × 10⁷ Hz; B0 = 1.03 × 10⁻⁸ T; B = (1.03 × 10⁻⁸ T) cos[(1.8 rad/m) y + (5.4 × 10⁸ rad/s) t] k

Solution

The phase (ky + ωt) increases with t for fixed phase requires y decreasing -> wave travels in -y. k = 1.8 rad/m so λ = 2*pi/1.8 = 3.49 m. ω = 5.4×10⁸ so ν = ω/(2*pi) = 5.4×10⁸/6.283 = 8.6×10⁷ Hz. B0 = E0/c = 3.1/(3×10⁸) = 1.03×10⁻⁸ T. With E along i and propagation along -j, B must be along k (so that E×B ∝ i×k = -j, the propagation direction). Hence B = (1.03×10⁻⁸) cos[(1.8)y + (5.4×10⁸)t] k.

Related JEE Advanced Physics questions

• A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 × 10⁸ m/s. The final momentum of object is
• A floodlight filtered to pass only red light produces a sinusoidal plane electromagnetic wave whose electric field component is given by Eₓ = 36 sin(1.20 * 10⁷ * z - 3.6 * 10¹⁵ * t) V/m. The average intensity of this beam is closest to sqrt(n) W/m², where n is an integer. Find n.
• The electric field of an electromagnetic wave is E = 20 sin(w*(t - x/c)) j V/m, where w is the angular frequency and c is the speed of light. Calculate the total electromagnetic energy stored in a volume of 5 * 10^(-4) m³. (Given: epsilon₀ = 8.85 * 10^(-12) C²/(N*m²))
• A plane electromagnetic wave of frequency 25 GHz propagates in vacuum along the +z direction. At a particular point in space and time, the magnetic field is B = 5 * 10^(-8) T in the +x direction. What is the corresponding electric field vector E? (Speed of light c = 3 * 10⁸ m/s)
• The electric field component of an electromagnetic wave in vacuum is given by E = (j-hat + b*k-hat) * 10⁻³ * sin[10⁷(x + 2y + 3z - beta*t)] in SI units. Using c = 3 * 10⁸ m/s, which of the following statements are correct?
• The magnetic field of a plane electromagnetic wave is given by B = 3 * 10^(-8) * sin[200*pi*(y + c*t)] * i_hat T, where c = 3 * 10⁸ m/s. What is the corresponding electric field?

⚔️ Practice JEE Advanced Physics free + battle 1v1 →