JEE Main 2022 · 28 June · morning · Single correct · +4 / −1
A radar sends an electromagnetic signal of electric field (E₀) = 2.25 V/m and magnetic field (B₀) = 1.5 × 10⁻⁸ T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time t = 0 from radar, then after how much time echo will reach to the radar?
- (a) 2.0 × 10⁻⁵ s
- (b) 4.0 × 10⁻⁵ s
- (c) 1.0 × 10⁻⁵ s
- (d) 8.0 × 10⁻⁵ s
Answer and solution
Answer (b) 4.0 × 10⁻⁵ s
Solution
Physics sir · 3 steps
The ratio of E to B gives the wave speed in this medium. Then cover 3 km out and 3 km back.
- Speed from fields. In any EM wave the field amplitudes are linked by E₀ = vB₀, where v is the wave speed in that medium. The signal is not in vacuum, so do not assume c.
v = E₀/B₀ = 2.25/(1.5 × 10⁻⁸) = 1.5 × 10⁸ m s⁻¹
- Total path. The echo goes to the target and comes back by the same path, so the distance is 2 × 3000 = 6000 m.
- So. t = 6000/(1.5 × 10⁸) = 4.0 × 10⁻⁵ s, which is option (b).
The idea to keep. For any EM wave, E₀/B₀ is the speed in that medium. Use it whenever the wave is not in vacuum, and for an echo always double the distance.
Answer from the NTA final answer key. Solution by PrepWiser.