I need to simulate the path a of particle in a magnetic and electrical field using the Larentz Force equation: d(m v)/dt = q[E(r) + v x B(r)]. I need to solve this equation numerically using euler's or any other method. at the end, by varing the time t, I will plot the path of the particle in the field. I just need a few examples of the solution of this equation at time 1 second, 2 senconds and 3 seconds. and also if the direction changes. thanks

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Related questions

A particle with a charge q = 1.60 x 10^-19 C, mass m = 2.00 x10^-27 kg, and an inital velocity v = v0(i+2j+2k), where v0=2.00 x10^5 m/s, enters a region with a uniform magnetic field B = B0j,where B0= 2.50T.

a) Calculate the force on this moving charge due to the magneticfield. The particle moves in a helical(cork-screw) path as ittravels in the y-direction.
b) Calculate the radius of the helical path.
c) How much time is required to make a complete revolution aboutthe y-axis?
d) How far has the particle traveled in the y-direction whilemaking one revolution around the y-axis?

Learning Goal: To apply Problem-SolvingStrategy20.1 Magnetic forces.

At a given instant, a particle with mass 5.00 x10^-3kg andcharge 3.5x10^-8 C has velocity ofmagnitude of2.0x10⁵m/s in the +ydirection. It is moving ina uniform magnetic field ofmagnitude 0.8T directed 40 degreesclockwise from theâx direction. What are the magnitude anddirectionof the magnetic force on the particle?

I found the angle between the velocity and magnitude ofthefield to be 50degrees, which is correct.

I calculated it as F=qvBsinÎ¸:

3.5x10^-8*2.0x10⁵m/s*0.8T*sin50=4.29x10^-3

Now I need help with this part. I couldn'tfind any equationthat break B down into itscomponents.

Part B

To check your answer, you should calculate the magnitude oftheforce using the second formula: F=qvB_{perpendicular}.Whatis the magnitude of B_{perpendicular}?

IsB_perp=B_x?

A metal bar of length L is attached to two vertical metalrailsas sketched in the figure below. The connections arefrictionless,but allow current to flow between the rails and thebar. There is aconstant horizontal magnetic field directedperpendicular to thearea enclosed by the bar and rails.