An isotropic point source emits light at wavelength 500 nm, at the rate of 185 W. A light detector is positioned 380 m from the source. What is the maximum rate ∂B/∂t at which the magnetic component of the light changes with time at the detector's location?

Explanation:

Given that

An isotropic point source emits light at a wavelength = 500 nm

Power = 185 W

Radius = 380 m

Let's first calculate the The intensity  of the wave , which is =

=

=  

=

Now;

The amplitude of the magnetic field is calculated afterwards by using poynting vector

i.e

The magnetic field wave equation can now be expressed as;

Taking the differentiation

The maximum value ;

where ;

then

the answer for apex is the lowest

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west