# What is the amplitude of the oscillating electric and magnetic field in the laser beam?

A typical helium-neon laser found in supermarket checkout scanners emits 633-nm-wavelength light in a 1.2mm diameter beam with a power of 1.5mW . Thanks in advance!

• Answers … E = 1.0 MV / m … B = 11 pT …

The amplitudes of the electric and magnetic fields in the laser beam can be

obtained from the intensity of the beam … for the electric field …

… I = Ea ² / [ 2 μ₀ c ] —> Ea ² = 2 μ₀ c I —> Ea = √ [ 2 μ₀ c I ] … where …

… I = P / [ π r ² ] = P / [ π ( ½ d ) ² ] = P / [ ¼ π d ² ] = 4 P / [ π d ² ] …

… where … d = beam diameter … that is …

… I = 4 ( 1.5 × 10 ⁻ ³ W ) / [ π ( 1.2 × 10 ⁻ ³ m ) ² ] = 1326 W / m ² … so that in

SI system … Ea = √ [ 2 μ₀ c I ] = √ [ 2 ( 4 π × 10 ⁻ ⁷ ) ( 3 × 10 ⁸ ) ( 1326 ) ]

…………………………………… = 1.0 × 10 ⁶ N / C = 1.0 × 10 ⁶ V / m = 1.0 MV / m ...

And since … Ea / Ba = c —> Ba = Ea / c = { √ [ 2 μ₀ c I ] } / c = √ [ 2 μ₀ I / c ]

… Ba = √ [ 2 ( 4 π × 10 ⁻ ⁷ ) ( 1326 ) / ( 3 × 10 ⁸ ) ]

…….. = 1.11 × 10 ⁻ ¹¹ T = 11 pT …