A radar sends an electromagnetic signal of electric field $$(E_0) = 2.25$$ V m$$^{-1}$$ and magnetic field $$(B_0) = 1.5 \times 10^{-8}$$ 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 radar sends an EM signal that strikes a target at 3 km distance and the echo returns. The velocity of an EM wave is given by: $$v = \frac{E_0}{B_0}$$. Substituting the given values yields $$v = \frac{2.25}{1.5 \times 10^{-8}} = 1.5 \times 10^8$$ m/s.

Since the signal travels to the target and back, the total distance covered is $$2 \times 3$$ km = $$6$$ km = $$6000$$ m.

Therefore, the time for the echo to return is calculated by $$t = \frac{\text{Total distance}}{v} = \frac{6000}{1.5 \times 10^8}$$, which simplifies to $$t = \frac{6 \times 10^3}{1.5 \times 10^8} = 4 \times 10^{-5}$$ s. The correct answer is Option B.