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2) (a) Show that the x-component of the Lorentz force, when written in terms of vector...
2) (a) Show that the x-component of the Lorentz force, when written in terms of vector...
2) (a) Show that the x-component of the Lorentz force, when written in terms of vector potentials as we did in class, can be expanded and then recast as o where U q-qA. Thus, show that Lagrange's equations still hold so long as U is taken to have this form, and that the Lagrangian for a non-relativistic particle in an electric and magnetic field can be written as equation (7.104) in the text. (b) Show from this Lagrangian and the...
a) Show that x-component of the Lorentz force, when written in terms of vector potentials as...
a) Show that x-component of the Lorentz force, when written in
terms of vector potentials as we did in class, can be expanded and
then recast as
where
Thus show that Lagrange’s equations still hold so long as U is
taken to have this form, and that the Lagrangian for a
non-relativistic particle in an electric and magnetic field can be
written as equation (7.104) in the text:
b) Show from this Lagrangian and the analysis in Section 7.8
that...
the same for the magnetic field vector B (in GR units, both vectors have the same...
the same for the magnetic field vector B (in GR units, both vectors have the same units where [E, E,, E.) are the components of the electric field vector É and [B,,B,,B.] are of kg . c-'m-': see box 4.2). Using this tensor, we can write a relativistically valid ver- sion of the Lorentz force law (which describes the total electromagnetic force acting on particle with charge q moving through an electromagnetic field), dp t = qFHV Nvalla and Gauss's...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equa...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equation of the form Ux = g , in which matrix U is an upper-triangular matrix. Show that the solution vector x may be obtained by a back-substitution algorithm, in the form Jekel (b) Iterative methods for solving Ax-b work by splitting matrix A into two...
2) (a) Show that the x-component of the Lorentz force, when written in terms of vector potentials as we did in class, can be expanded and then recast as o where U q-qA. Thus, show that Lagrange's equations still hold so long as U is taken to have this form, and that the Lagrangian for a non-relativistic particle in an electric and magnetic field can be written as equation (7.104) in the text. (b) Show from this Lagrangian and the...
a) Show that x-component of the Lorentz force, when written in
terms of vector potentials as we did in class, can be expanded and
then recast as
where
Thus show that Lagrange’s equations still hold so long as U is
taken to have this form, and that the Lagrangian for a
non-relativistic particle in an electric and magnetic field can be
written as equation (7.104) in the text:
b) Show from this Lagrangian and the analysis in Section 7.8
that...
the same for the magnetic field vector B (in GR units, both vectors have the same units where [E, E,, E.) are the components of the electric field vector É and [B,,B,,B.] are of kg . c-'m-': see box 4.2). Using this tensor, we can write a relativistically valid ver- sion of the Lorentz force law (which describes the total electromagnetic force acting on particle with charge q moving through an electromagnetic field), dp t = qFHV Nvalla and Gauss's...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equation of the form Ux = g , in which matrix U is an upper-triangular matrix. Show that the solution vector x may be obtained by a back-substitution algorithm, in the form Jekel (b) Iterative methods for solving Ax-b work by splitting matrix A into two...
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