C. Suppose the E- and B-fields of an electromagnetic plane wave traveling in free space are...

Transcribed Image Text:

C. Suppose the E- and B-fields of an electromagnetic plane wave traveling in free space are given by the following expressions, where the vectors E, and B. are real constants. (1)(,t) = exp[i(k wt)] (2) B(r,t) = B exp[i(k-wt)] Using expression (1) for the electric field, what is the partial derivative with respect to x of the x-component of E(F,t)? Ex (F.1)=? Use the above result to find an expression for the divergence of for this plane wave, written in terms of a dot-product of the vectors K and . x . , . , + + dz = According to Maxwell's equations VE = p/. What is the divergence of the electric field equal to for a plane wave traveling in vacuum? V.E=? According to Maxwell's equations, what is the divergence of B for a plane wave traveling in vacuum? V-B =? Using the information on this page, what can you conclude about the direction of & B relative to the vector K ? C. Suppose the E- and B-fields of an electromagnetic plane wave traveling in free space are given by the following expressions, where the vectors E, and B. are real constants. (1)(,t) = exp[i(k wt)] (2) B(r,t) = B exp[i(k-wt)] Using expression (1) for the electric field, what is the partial derivative with respect to x of the x-component of E(F,t)? Ex (F.1)=? Use the above result to find an expression for the divergence of for this plane wave, written in terms of a dot-product of the vectors K and . x . , . , + + dz = According to Maxwell's equations VE = p/. What is the divergence of the electric field equal to for a plane wave traveling in vacuum? V.E=? According to Maxwell's equations, what is the divergence of B for a plane wave traveling in vacuum? V-B =? Using the information on this page, what can you conclude about the direction of & B relative to the vector K ?