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Exercise:
The amplitudes of the electric and magnetic field vectors in an electromagnetic wave propagating along the x direction are vectors in the xy plane. abcliste abc For a magnetic field vector vecB pmatrix B_x B_y pmatrix find the components of the corresponding electric field vector. abc For an electric field vector vecE pmatrix E_x E_y pmatrix find the components of the corresponding magnetic field vector. abcliste

Solution:
abcliste abc The electric field vector is given by the relation vec E vec B cross vec c. It follows vec E pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_y c - - B_x c B_x - B_y pmatrix pmatrix B_y c -B_x c pmatrix c pmatrix B_y -B_x pmatrix We can easily verify that vec E is perpicular to vec B and that E B c: vec E vec B B_x B_y + B_y -B_x B_x B_y - B_x B_y E absvec E sqrtE_x^ + E_y^ sqrtc B_y^+-c B_x^ sqrtc^ B_y^ + B_x^ c sqrtB_x^+B_y^ c absvec B c B abc abcliste
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Exercise:
The amplitudes of the electric and magnetic field vectors in an electromagnetic wave propagating along the x direction are vectors in the xy plane. abcliste abc For a magnetic field vector vecB pmatrix B_x B_y pmatrix find the components of the corresponding electric field vector. abc For an electric field vector vecE pmatrix E_x E_y pmatrix find the components of the corresponding magnetic field vector. abcliste

Solution:
abcliste abc The electric field vector is given by the relation vec E vec B cross vec c. It follows vec E pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_y c - - B_x c B_x - B_y pmatrix pmatrix B_y c -B_x c pmatrix c pmatrix B_y -B_x pmatrix We can easily verify that vec E is perpicular to vec B and that E B c: vec E vec B B_x B_y + B_y -B_x B_x B_y - B_x B_y E absvec E sqrtE_x^ + E_y^ sqrtc B_y^+-c B_x^ sqrtc^ B_y^ + B_x^ c sqrtB_x^+B_y^ c absvec B c B abc abcliste
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Attributes & Decorations
Branches
Electromagnetic Waves
Tags
electric field, magnetic field, vector
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration