Since the electric field is perpendicular to the magnetic field, their dot product is zero.

E.B = 0

(100 î+200 ĵ−50 kˆ).(5.2 î−8.3 ĵ - b kˆ) = 0

[(100)(5.2) + (200)(-8.3) + (-50)(-b)] = 0

520 - 1660 + 50b = 0

b = 22.8

⇒ B = (5.2 î−8.3 ĵ - 22.8 kˆ) T

The poynting vector is;

S = μ0-1E x B

S = μ0-1{[(200)(-22.8)-(-50)(-8.3)]î - [(100)(-22.8)-(-50)(5.2)]ĵ + [(100)(-8.3)-(200)(5.2)]kˆ}

S = (4π × 10-7 H/m)-1(103)(-4.9 î + 2.0 ĵ - 1.9 kˆ) W/m2

S = - (3.9 × 109) î + (1.6 × 109) ĵ - (1.5 × 109) kˆ W/m2

Energy Carried by Electromagnetic Waves Practice Problems