Exams › JEE Advanced › Physics

The magnetic field of a plane electromagnetic wave is given by B = 3 * 10⁻⁸ * sin[200*pi*(y + ct)] i_hat (in Tesla), where c = 3 * 10⁸ m/s. What is the corresponding electric field?

1. E = -10⁻⁶ * sin[200*pi*(y + ct)] k_hat V/m
2. E = -9 * sin[200*pi*(y + ct)] k_hat V/m
3. E = 9 * sin[200*pi*(y + ct)] k_hat V/m
4. E = 3 * 10⁻⁸ * sin[200*pi*(y + ct)] k_hat V/m

Correct answer: E = -9 * sin[200*pi*(y + ct)] k_hat V/m

Solution

Amplitude of E: E₀ = c * B₀ = 3*10⁸ * 3*10⁻⁸ = 9 V/m. Wave propagation direction: argument (y + ct) means wave travels in -y direction (since at t=0, the wave front is at y=0, and at t>0 the same phase is at y = -ct, moving in -y). Unit vector of propagation: k_hat_prop = -j_hat. Relationship: E cross B must point in direction of propagation. E_hat cross B_hat = k_hat_prop = -j_hat. B is along i_hat. If E is along -k_hat (negative z): (-k_hat) cross (i_hat) = -(k_hat cross i_hat) = -(j_hat) = -j_hat. Yes! This works. So E = -9 * sin[200*pi*(y+ct)] k_hat V/m.

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 →