Physics

Physics

Problem

The electric field of a plane electromagnetic wave in vacuum is given by E(z,t)=75 N/C  j^  cos⁡(kz+ωt)\displaystyle \mathbf{E}(z,t)=75\,\text{N/C}\;\hat{j}\;\cos(kz+\omega t), where kk and ω\omega are positive constants. Which of the following correctly states the direction of propagation and an appropriate magnetic–field expression consistent with Maxwell’s equations? a) Propagates in the +z+z–direction; B(z,t)=75c (−i^) cos⁡(kz+ωt)\displaystyle \mathbf{B}(z,t)=\frac{75}{c}\,(-\hat i)\,\cos(kz+\omega t) b) Propagates in the −z-z–direction; B(z,t)=75c i^ cos⁡(kz−ωt)\displaystyle \mathbf{B}(z,t)=\frac{75}{c}\,\hat i\,\cos(kz-\omega t) c) Propagates in the −z-z–direction; B(z,t)=75c i^ cos⁡(kz+ωt)\displaystyle \mathbf{B}(z,t)=\frac{75}{c}\,\hat i\,\cos(kz+\omega t) d) Propagates in the −z-z–direction; B(z,t)=75c k^ cos⁡(kz+ωt)\displaystyle \mathbf{B}(z,t)=\frac{75}{c}\,\hat{k}\,\cos(kz+\omega t)

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