A radio transmitter sends out 60 W of radiation. Assuming that the radiation is uniform on a sphere with the transmitter at its centre, the intensity (in W/m2) of the wave at a distance 12 km is

Question

A radio transmitter sends out 60 W of radiation. Assuming that the radiation is uniform on a sphere with the transmitter at its centre, the intensity (in W/m2) of the wave at a distance 12 km is (A) 5.33 × 10-8 (B) 3.33 × 10-6 (C) 2.12 × 10-8 (D) 6.66 × 10-8

Tardigrade Admin · Accepted Answer

Power of transmitted radiation, PT=60 W. ∴ Intensity of wave, I=(PT/A) ∵ A=4 π R2 4 π(12 Km )2 (∵ R=12 km given ) ⇒ A=4 π × 144 × 106 ∴ I=(60/4 π × 144 × 106) =3.31 × 10-8 W / M 2

Q. A radio transmitter sends out $60 W$ of radiation. Assuming that the radiation is uniform on a sphere with the transmitter at its centre, the intensity (in $W / m^{2}$ ) of the wave at a distance $12 km$ is

$5.33 \times 1 0^{- 8}$

$3.33 \times 1 0^{- 6}$

$2.12 \times 1 0^{- 8}$

$6.66 \times 1 0^{- 8}$

$3.33 \times 1 0^{- 8}$

Power of transmitted radiation, $P_{T} = 60 W$ .
$∴$ Intensity of wave, $I = \frac{P _{T}}{A}$
$∵ A = 4 π R^{2}$
$4 π (12 K m)^{2} (∵ R = 12 km$ given $)$
$\Rightarrow A = 4 π \times 144 \times 1 0^{6}$
$∴ I = \frac{60}{4 π \times 144 \times 1 0 ^{6}}$
$= 3.31 \times 1 0^{- 8} W / M^{2}$

Q. A radio transmitter sends out 60W of radiation. Assuming that the radiation is uniform on a sphere with the transmitter at its centre, the intensity (in W/m2) of the wave at a distance 12km is

5.33×10−8

3.33×10−6

2.12×10−8

6.66×10−8

3.33×10−8