2. Maxwell's equations relating the electric field E and the magnetic field H as they vary withtime in a vacuum are given as follows:divE = 0(1)divÅ(2)curlE(3)c ôt1 DEcurlH(4)с дёwhere c is the speed of light (pretty fast).(a) Using Maxwell's equations, showV × (V × Ē)(5)c2 Ət2(b) Using Maxwell's equations, show(V . V)Ẻ =(6)c2 at2 *You may find vector operator identity 3.38 from your textbook helpful:V x (V × F) = V(V· F) – V²F.(7) V × (V × F) = V(V · F) – v²F.(7)(c) Use the results of the two parts above to show thatAẼ = 0.(8)c2 Ət?(Such a relation between the time and space dependence of a function is called the waveequation. You've probably seen it before, though maybe not in this specific form.)

Given that: Maxwell's equations are given as: a)∇→×E→=-1cδH→δtNow taking curl boyth sides:∇→×(∇→×E)→=1cδ(∇→×H→)δt∇→×(∇→×E)→=-1cδδt(1cδE→δt)∇→×(∇→×E)→=-1c2δ2E→δt2b)∇→×(∇→×E)→=∇→(∇→.E)→-∇2E→-1c2δ2E→δt2=∇→(0)-∇2E→∇2E→=1c2δ2E→δt2(∇→.∇→)E→=1c2δ2E→δt2c)Hence:∇2E→=1c2δ2E→δt21c2δ2E→δt2-∇2E→=01c2δ2E→δt2-∆E→=0

Answered: Maxwell's equations relating the…