Exams › JEE Advanced › Physics

In a material with conductivity sigma = 5.0 S/m and relative permittivity epsilon_r = 1, the electric field is E = 250 sin(10¹⁰ * t) V/m. Determine the conduction current density Jc, the displacement current density Jd, and the frequency f at which their amplitudes are equal.

1. Jc = 1250 sin(10¹⁰ t) A/m²; Jd = 22.1 cos(10¹⁰ t) A/m²; f = 90 GHz
2. Jc = 22.1 cos(10¹⁰ t) A/m²; Jd = 1250 sin(10¹⁰ t) A/m²; f = 90 GHz
3. Jc = 1250 sin(10¹⁰ t) A/m²; Jd = 22.1 sin(10¹⁰ t) A/m²; f = 50 GHz
4. Jc = 1250 cos(10¹⁰ t) A/m²; Jd = 22.1 cos(10¹⁰ t) A/m²; f = 50 GHz

Correct answer: Jc = 1250 sin(10¹⁰ t) A/m²; Jd = 22.1 cos(10¹⁰ t) A/m²; f = 90 GHz

Solution

Jc = 5 * 250 sin(10¹⁰ t) = 1250 sin(10¹⁰ t) A/m². Jd = epsilon₀ * dE/dt = 8.854e-12 * 250 * 10¹⁰ * cos(10¹⁰ t) = 22.1 cos(10¹⁰ t) A/m². For equal amplitudes: sigma = omega*epsilon₀ -> f = sigma/(2*pi*epsilon₀) = 5/(2*pi*8.854e-12) approx 90 GHz.

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 →