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A large, flat sheet carries a uniformly distributed electric current with current per unit width J. This current creates a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude B = Hos If the current is in the y direction and oscillates in time according to Jmay (cos wt)j = Jma(cos (-wt)lj the sheet radiates an electromagnetic wave. The figure below shows such a wave emitted from one point on the sheet chosen to be the origin. Such electromagnetic waves are emitted from all points on the sheet. The magnetic field of the wave to the right of the sheet is described by the wave function B = -Hmau[sin (kx – we)j&. (a) Find the wave function for the electric field of the wave to the right of the sheet. (Use the following as necessary: Hg, c for the speed of light, Imax k, x, w, and t.) E = (b) Find the Poynting vector as a function of x and t. (Use the following as necessary: Hor c for the speed of light, max k, x, w, and t.) 5 = (c) Find the intensity of the wave. (Use the following as necessary: Ho, c for the speed of light, Jmax k, x, w, and t.) I = (d) If the sheet is to emit radiation each direction (normal to the plane of the sheet) with intensity 409 W/m, what maximum value of sinusoidal current density required? A/m

A large, flat sheet carries a uniformly distributed electric current with current per unit width J. This current creates a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude B = Hos If the current is in the y direction and oscillates in time according to Jmay (cos wt)j = Jma(cos (-wt)lj the sheet radiates an electromagnetic wave. The figure below shows such a wave emitted from one point on the sheet chosen to be the origin. Such electromagnetic waves are emitted from all points on the sheet. The magnetic field of the wave to the right of the sheet is described by the wave function B = -Hmau[sin (kx – we)j&. (a) Find the wave function for the electric field of the wave to the right of the sheet. (Use the following as necessary: Hg, c for the speed of light, Imax k, x, w, and t.) E = (b) Find the Poynting vector as a function of x and t. (Use the following as necessary: Hor c for the speed of light, max k, x, w, and t.) 5 = (c) Find the intensity of the wave. (Use the following as necessary: Ho, c for the speed of light, Jmax k, x, w, and t.) I = (d) If the sheet is to emit radiation each direction (normal to the plane of the sheet) with intensity 409 W/m, what maximum value of sinusoidal current density required? A/m

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A large, flat sheet carries a uniformly distributed electric current with current per unit width J.. This current creates a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude B = If the current is in the y direction and oscillates in time according to Imax (cos wt)j = Jmax[cos (-wt)]j the sheet radiates an electromagnetic wave. The figure below shows such a wave emitted from one point on the sheet chosen to be the origin. Such electromagnetic waves are emitted from all points on the sheet. The magnetic field of the wave to the right of the sheet is described by the wave function 1 -글어man[sin (kex-aut) k. (a) Find the wave function for the electric field of the wave to the right of the sheet. (Use the following as necessary: uo, c for the speed of light, Jma, k, x, w, and t.) E = (b) Find the Poynting vector as a function of x and t. (Use the following as necessary: Hn, c for the speed of light, Jmax k, x, w, and t.) 3 = (c) Find the intensity of the wave. (Use the following as necessary: Ho, c for the speed of light, Jmax, k, x, w, and t.) I = (d) If the sheet is to emit radiation in each direction (normal to the plane of the sheet) with intensity 409 W/m2, what maximum value of sinusoidal current density is required? A/m
Transcribed Image Text:A large, flat sheet carries a uniformly distributed electric current with current per unit width J.. This current creates a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude B = If the current is in the y direction and oscillates in time according to Imax (cos wt)j = Jmax[cos (-wt)]j the sheet radiates an electromagnetic wave. The figure below shows such a wave emitted from one point on the sheet chosen to be the origin. Such electromagnetic waves are emitted from all points on the sheet. The magnetic field of the wave to the right of the sheet is described by the wave function 1 -글어man[sin (kex-aut) k. (a) Find the wave function for the electric field of the wave to the right of the sheet. (Use the following as necessary: uo, c for the speed of light, Jma, k, x, w, and t.) E = (b) Find the Poynting vector as a function of x and t. (Use the following as necessary: Hn, c for the speed of light, Jmax k, x, w, and t.) 3 = (c) Find the intensity of the wave. (Use the following as necessary: Ho, c for the speed of light, Jmax, k, x, w, and t.) I = (d) If the sheet is to emit radiation in each direction (normal to the plane of the sheet) with intensity 409 W/m2, what maximum value of sinusoidal current density is required? A/m
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