Question

At some instant and location the electric field associated with an electromagnetic wave in vacuum has the strength 77.9 V/m. Find the magnetic field strength, the energy density, and the power flow per unit area, all at the same instant and location. Magnetic field: T Energy density: J/m^3 Power flow per unit area: W/m^2

Answer 1

magnetic field strength

=electric fieldstrength/speed of light

=77.9/(3*10^8)=2.5967*10(-7) T

part B:

energy density=0.5*epsilon*E^2+0.5*(B^2/mu)

where E=electrical field strength

B=magnetic field strength

epsilon=electrical permitivity

mu=magnetic permeability

then energy density=0.5*8.85*10^(-12)*77.9^2+0.5*(2.5967^2*10^(-14)/(4*pi*10^(-7)))=5.3682*10^(-8) J/m^3

part c:

power flow per unit area=energy density*speed of light

=16.104 W/m^2

Answer 2

Solution: 

Given: Electric field E = 77.9 V/m

To find magnetic field strength we know

Ratio of electric field and magnetic field strength = speed of light 

i.e. E/B = c

therefore  B = E/c = 77.9 V/m / (3x10⁸ m/s)

Magnetic field strength B = 2.596 x 10^-7 T ------------Answer

 

Total energy density u = (1/2) x $\varepsilon$₀ x E² + ( 1/2$\mu$₀ ) B²

                               = 0.5 x (8.854 x 10^-12 C² / N-m² ) x ( 77.9 V/m )² + (1 / (2x 4$\pi$ x10^-7 H/m) ) x (2.596 x 10^-7 T)²

                                   u = 5.578 x 10^-8 J/m³  --------------- Answer

 

Power flow per unit area or intensity = Ennergy density x sped of light

Power flow per unit area = ( 5.424 x 10^-8 J/m³ ) x (3 x10⁸ m/s)

Power flow per unit area  = 16.735 W/m² ------------------------Answer

Answer 3

Solution: 

Given: Electric field E = 77.9 V/m

To find magnetic field strength we know

Ratio of electric field and magnetic field strength = speed of light 

i.e. E/B = c

therefore  B = E/c = 77.9 V/m / (3x108 m/s)

Magnetic field strength B = 2.596 x 10-7 T ------------Answer

 

Total energy density u = (1/2) x $\varepsilon$0 x E2 + ( 1/2$\mu$0 ) B2

                           = 0.5 x (8.854 x 10-12 C2 / N-m2 ) x ( 77.9 V/m )2 + (1 / (2x 4$\pi$ x10-

7 H/m) ) x (2.596 x 10-7 T)2

                                   u = 5.3679 x 10-8 J/m3  --------------- Answer

 

Power flow per unit area or intensity = Ennergy density x sped of light

Power flow per unit area = ( 5.424 x 10-8 J/m3 ) x (3 x108 m/s)

Power flow per unit area  = 16.103 W/m2 ------------------------Answer