JEE Main · 2022 · 28 Jun 2022 · Shift 1 · EM Waves

A radar sends an electromagnetic signal of electric field

(E_{0}) = 2.25 V / m

and magnetic field

(B_{0}) = 1.5 \times 1 0^{- 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) $2.0 \times 1 0^{- 5} s$
(B) $4.0 \times 1 0^{- 5} s$ ✓ Correct
(C) $1.0 \times 1 0^{- 5} s$
(D) $8.0 \times 1 0^{- 5} s$

Answer: (B)

Solution

The velocity of the electromagnetic wave in the medium is given by

c = \frac{E _{0}}{B _{0}} = \frac{2.25}{1.5 \times 1 0 ^{- 8}} = 1.5 \times 1 0^{8} m/s

. The total distance traveled by the signal is twice the distance to the target (to and back):

d = 2 \times 3 \times 1 0^{3} = 6 \times 1 0^{3} m

. The time taken is

t = \frac{d}{c} = \frac{6 \times 1 0 ^{3}}{1.5 \times 1 0 ^{8}} = 4 \times 1 0^{- 5} s

. Therefore, the answer is (B).

JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Single correct option

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JEE Main · 2022 · 28 Jun 2022 · Shift 1 · EM Waves

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