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https://texercises.com/exercise/magnetic-force-as-a-vector/
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Exercise:
An electron with velocity vecv enters a uniform magnetic field vecB. With respect to the axis of a Cartesian coordinate system the two vectors can be written as vecv leftmatrixv_xv_yv_zmatrixright leftmatrixvxMX vyMX vzMXmatrixright unitmegam/s vecB leftmatrixB_xB_yB_zmatrixright leftmatrixBxmX BymX BzmXmatrixright unitmilliT abcliste abc Calculate the components and the magnitude of the magnetic force vector acting on the electron. abc Explain why it is impossible for an electron to experience a force in the direction of the z-axis no matter what direction its velocity vector has. abcliste

Solution:
abcliste abc The force vecF is given by vecF q vecvcrossvecB q left matrixv_y B_z-v_z B_y v_z B_x-v_x B_z v_x B_y-v_y B_x matrix right qtimes left matrixvyMX BzmX-vzMX BymX vzMX BxmX-vxMX BzmX vxMX BymX-vyMX BxmX matrix right unitkilom/stimesT left matrix FfxX FfyX FfzX matrix rightunitfemtonewton approx resultleft matrix FxP- FyP- FzP- matrixright The magnitude of the force vector is absvecFFabsF sqrtleftFfxX^+FfyX^+FfzX^rightunitfemtonewton Fabs approx resultFabsP- abc The magnetic force is always perpicular to both the velocity vecv and the magnetic field vecB. In order to experience a force in the direction of the z-axis the velocity and the magnetic field have to be in the xy-plane. Since vecB has a non-vanishing z component this is obviously not the case. abcliste
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Exercise:
An electron with velocity vecv enters a uniform magnetic field vecB. With respect to the axis of a Cartesian coordinate system the two vectors can be written as vecv leftmatrixv_xv_yv_zmatrixright leftmatrixvxMX vyMX vzMXmatrixright unitmegam/s vecB leftmatrixB_xB_yB_zmatrixright leftmatrixBxmX BymX BzmXmatrixright unitmilliT abcliste abc Calculate the components and the magnitude of the magnetic force vector acting on the electron. abc Explain why it is impossible for an electron to experience a force in the direction of the z-axis no matter what direction its velocity vector has. abcliste

Solution:
abcliste abc The force vecF is given by vecF q vecvcrossvecB q left matrixv_y B_z-v_z B_y v_z B_x-v_x B_z v_x B_y-v_y B_x matrix right qtimes left matrixvyMX BzmX-vzMX BymX vzMX BxmX-vxMX BzmX vxMX BymX-vyMX BxmX matrix right unitkilom/stimesT left matrix FfxX FfyX FfzX matrix rightunitfemtonewton approx resultleft matrix FxP- FyP- FzP- matrixright The magnitude of the force vector is absvecFFabsF sqrtleftFfxX^+FfyX^+FfzX^rightunitfemtonewton Fabs approx resultFabsP- abc The magnetic force is always perpicular to both the velocity vecv and the magnetic field vecB. In order to experience a force in the direction of the z-axis the velocity and the magnetic field have to be in the xy-plane. Since vecB has a non-vanishing z component this is obviously not the case. abcliste
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Branches
Magnetism
Tags
cross product, electron, magnetic force, vector geometry
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Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Decoration
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