Question

An isotropic point source emits light at wavelength 510 nm, at the rate of 170 W. A light detector is positioned 410 m from the source. What is the maximum rate dB/dt at which the magnetic component of the light changes with time at the detector's location? The speed of light is c = 3 × 108 m/s, and μ0 = 4π × 10-7 H/m.

Answer 1

`(dB)/(dt) = 3.03 * 10^6 T/s`

Step-by-step explanation:

As we know that the power emitted by the source is given as

`P = 170 W`

now we know that

`P = (N)/(t) ((hc)/(\lambda))`

now we know that energy density is given as

`u = (B^2)/(2\mu_0) + (\epsilon_0 E^2)/(2)`

now we have

`E = B c`

`u = (B^2)/(2\mu_0)`

intensity is defined as

`I = (P)/(A)`

now we have

`(I)/(c) = u = (B^2)/(2\mu_0)`[/tex]

now we have

`(dB)/(dt) = \omega B`

`(dB)/(dt) = (2\pi c B)/(\lambda)`

`(dB)/(dt) = (2\pi c √(2\mu_0 I))/(\lambda\sqrt c)`

here we have

`I = (P)/(4\pi r^2)`

`I = (170)/(4\pi (410)^2)`

`I = 8.05 * 10^(-5)`

now we have

`(dB)/(dt) = \frac{2\pi\sqrt{2\mu_0 c (8.05 * 10^(-5))}}{(510 nm)}`

`(dB)/(dt) = 3.03 * 10^6 T/s`