Spectroscopy

Step 1: Formula for intensity and magnetic field.
The intensity

I

of an electromagnetic wave is related to the amplitude of the electric and magnetic fields by:

I%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cepsilon_0%20c%20E_0%5E2%2C

where

E_0

is the amplitude of the electric field. The amplitude of the magnetic field

B_0

is related to the amplitude of the electric field by:

B_0%20%3D%20%5Cfrac%7BE_0%7D%7Bc%7D.

Step 2: Calculate the electric field.
Rearranging the intensity formula to solve for

E_0

E_0%20%3D%20%5Csqrt%7B%5Cfrac%7B2I%7D%7B%5Cepsilon_0%20c%7D%7D.

Substituting the given values:

E_0%20%3D%20%5Csqrt%7B%5Cfrac%7B2%20%5Ctimes%204%20%5Ctimes%2010%5E%7B14%7D%7D%7B8.85%20%5Ctimes%2010%5E%7B-12%7D%20%5Ctimes%203%20%5Ctimes%2010%5E8%7D%7D%20%5Capprox%206.6%20%5Ctimes%2010%5E3%20%5C%2C%20%5Ctext%7BV%2Fm%7D.

Step 3: Calculate the magnetic field.
Now, using the relation between

E_0

and

B_0

B_0%20%3D%20%5Cfrac%7BE_0%7D%7Bc%7D%20%3D%20%5Cfrac%7B6.6%20%5Ctimes%2010%5E3%7D%7B3%20%5Ctimes%2010%5E8%7D%20%5Capprox%201.83%20%5C%2C%20%5Ctext%7BTesla%7D.

Final Answer:

%5Cboxed%7B1.83%20%5C%2C%20%5Ctext%7BTesla%7D%7D.

Chapter Questions
1 MCQs