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Exercise:
The amplitude of the magnetic field vector of an electromagnetic wave propagating along the z axis is vec B pmatrix B_x B_y pmatrix Express the amplitude of the corresponding electric field vector and the Poynting vector in terms of B_x B_y and the speed of light.

Solution:
The electric field vector is vec E vec Bcross vec c pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_yc- -B_xc - pmatrix cpmatrix B_y -B_x pmatrix The two field vectors are perpicular to each other: vec E vec B c pmatrix B_y -B_x pmatrix pmatrix B_x B_y pmatrix cB_yB_x-B_xB_y The amplitude of the Poynting vector is vec S_ fracmu_vec Ecrossvec B fraccmu_pmatrix B_y -B_x pmatrix cross pmatrix B_x B_y pmatrix fraccmu_pmatrix B_yB_y--B_xB_x pmatrix fraccmu_ pmatrix B_y^+B_x^ pmatrix fraccmu_ pmatrix B_^ pmatrix As expected the Poynting vector has the same direction as the direction of propagation. Its amplitude is equal to S_ fracc B_^mu_ fracmu_rE_ B_
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Exercise:
The amplitude of the magnetic field vector of an electromagnetic wave propagating along the z axis is vec B pmatrix B_x B_y pmatrix Express the amplitude of the corresponding electric field vector and the Poynting vector in terms of B_x B_y and the speed of light.

Solution:
The electric field vector is vec E vec Bcross vec c pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_yc- -B_xc - pmatrix cpmatrix B_y -B_x pmatrix The two field vectors are perpicular to each other: vec E vec B c pmatrix B_y -B_x pmatrix pmatrix B_x B_y pmatrix cB_yB_x-B_xB_y The amplitude of the Poynting vector is vec S_ fracmu_vec Ecrossvec B fraccmu_pmatrix B_y -B_x pmatrix cross pmatrix B_x B_y pmatrix fraccmu_pmatrix B_yB_y--B_xB_x pmatrix fraccmu_ pmatrix B_y^+B_x^ pmatrix fraccmu_ pmatrix B_^ pmatrix As expected the Poynting vector has the same direction as the direction of propagation. Its amplitude is equal to S_ fracc B_^mu_ fracmu_rE_ B_
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Attributes & Decorations
Branches
Electromagnetic Waves
Tags
electric field, magnetic field, poynting vector
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration
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