Question

In a region of free space, the electric field at an instant of time is = [(26.0) i+ (-52.0) j+ (65.0)k] N/C, and the magnetic field is = [(0.080) i+ (0.290) j+(0.200)k] µT.

(a) Show that the two fields are perpendicular to each other by calculating the following quantities.
ExBx =.......... N µT/C
EyBy =......... N µT/C
EzBz =......... N µT/C
ExBx + EyBy + EzBz =......... N µT/C

(b) Determine the component representation of the Poynting vector for these fields. Use three decimal places.
S = ......... W/m2

Answer 1

E = [(26.0) i + (-52.0) j + (65.0) k] N/C,

B = [(0.160) i + (0.580) j + (0.400) k] µT.

(a) Show that the two fields are perpendicular to each other by calculating the following quantities.

ExBx = 26.0*0.160 = 4.16 N µT/C

EyBy = (-52.0)*0.580 = -30.16 N µT/C

EzBz = 65.0*0.400 = 26.0 N µT/C

E dot B = ExBx + EyBy + EzBz = 0

when the dot product of 2 vectors is zero, these 2 vectors are perpendicular to each other.

 

(b) Determine the component representation of the Poynting vector for these fields. Poynting vector = E cross B/mu_0 =

E cross B =   = (-58.5 i + 0 j + 23.4 k) N µT/C

so Poynting vector = (-46.6 i + 0 j + 18.6 k) W/m^2