Question

A light source radiates 60.0 W of single-wavelength sinusoidal light uniformly in all directions. What is the amplitude of the magnetic field of this light at a distance of 0.700 m from the bulb?

Answer 1

To solve this problem it is necessary to take into account the concepts of Intensity as a function of Power and the definition of magnetic field.

The intensity depending on the power is defined as

$I = \frac{P}{4\pi r^2},$

Where

P = Power

r = Radius

Replacing the values that we have,

$I = \frac{60}{(4*\pi (0.7)^2)}$

$I = 9.75 Watt/m^2$

The definition of intensity tells us that,

$I = \frac{1}{2}\frac{B_o^2 c}{\mu}$

Where,

$B_0 =$Magnetic field

$\mu =$ Permeability constant

c = Speed velocity

Then replacing with our values we have,

$9.75 = \frac{Bo^2 (3*10^8)}{(4\pi*10^{-7})}$

Re-arrange to find the magnetic Field B_0

$B_o = 2.86*10^{-7} T$

Therefore the amplitude of the magnetic field of this light is $B_o = 2.86*10^{-7} T$