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I see your point I guess but it comes the same way as I did right i mean. Your equations solutions and my solutions has to be same(if they are correct)Ray Vickson said:
I see your point I guess but it comes the same way as I did right i mean. Your equations solutions and my solutions has to be same(if they are correct)Ray Vickson said:One way to do it is to write ##v_e(t) = w_e(t) + a_e + c_e t,##, ##v_b(t) = w_b(t) + a_b + c_b t,## and ##v_x(t) = w_x(t) + a_x + c_x t, ## where the a's and c's are constants. When you put those forms into the 3 DEs, you will get DEs for the w(t)s that have some constants in them. By choosing the a's and c's appropriately, you can eliminate all the constants and be left with the homogeneous system
$$
\begin{array}{rcr}
m \dot{w_e} &=& -q \alpha w_x \\
m \dot{w_b} &=& q \beta w_x \\
m \dot{w_x} &=& q w_e
\end{array}
$$
in ##w_e, w_b, w_x##. The initial conditions on the ##v(t)##s translate into initial conditions on the ##w(t)##s, which then fixes the solution uniquely.
The Lorentz force-differential equation is a mathematical formula that describes the force experienced by a charged particle in an electric and magnetic field. It is given by F = q(E + v x B), where F is the force, q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.
The solution to the Lorentz force-differential equation depends on the specific scenario and boundary conditions. In general, it involves solving a system of differential equations using mathematical techniques such as separation of variables, integration, and substitution.
The Lorentz force-differential equation is significant because it helps us understand and predict the behavior of charged particles in electric and magnetic fields. It is the basis for many important technologies such as electric motors, generators, and particle accelerators.
The Lorentz force-differential equation has numerous applications in physics and engineering. It is used to study the motion of charged particles in particle accelerators, to design and optimize electric motors and generators, and to understand the behavior of plasma in fusion reactors.
The Lorentz force-differential equation assumes that the charged particle is point-like, has a constant charge, and is not affected by other forces besides the electric and magnetic fields. It also assumes that the electric and magnetic fields are constant and do not change over time.