Question

An energy saving lamp with a power of P = 11 W emits an electromagnetic wave uniformly in all directions. Calculate the wave at a distance of r = 3 m from the lamp

(a) the intensity

(b) the radiation pressure

(c) electric field amplitude

(d) the amplitude of the magnetic field

Answer 1

a) intensity is defined by power per unit area,

For the given distance of 3m the surface area of the imaginary sphere of 3m radius will be 4*π*3² = 4*3.14*9 = 113m²

Therefore, intensity= 11/113 = 0.097 W/m^{​​​​​​2}​​​

b) radiation pressure: pressure is defined as force per unit area and power is defined as force into velocity

Therefore, radiation pressure can also be given by:

Power/(area*velocity)

Since it is electromagnetic wave, it's speed is 3*10⁸m/s

Therefore, radiation pressure = intensity/ speed of light

= 0.097/(3*10⁸)

= 3.2*10^-10 N/m^{​​​​​​2}​​​

C)

Intensity for an electromagnetic wave is given by:

I = (0.5)_o(E_{​​​​​​o})²*c

Where _o is permittivity of free space, c is speed of light and E_{​​​​​​o} is the magnitude of electric field,

Therefore,

E_{​​​​​​O} = {2*I/(_o*c)}^0.5 = { 2*0.097/(8.85*10^-12*3*10⁸)}^0.5

E_{​​​​​​O} = 8.54 N/C

d) Amplitude of magnetic field: we have a relationship between amplitude of electric & magnetic fields

E_{​​​​​​O} = c*B_{​​​​​​o}

Therefore, B_{​​​​​o} = E_{​​​​​​o}/c = 8.54/(3*10⁸) = 2.85*10^-8 Tesla