When an electron passes through the origin (x = 0, y = 0, z = 0), its velocity h

Question

When an electron passes through the origin (x = 0, y = 0, z = 0), its velocity has components of vsubx = 0 m/s, vsuby = +5000 m/s, and vsubz = +1000 m/s. Now, two forces act on the electron, one from the same magnetic field we had above, and the other from a uniform electric field that is in the positive z-direction with a magnitude of 2000 N/C.

a.After a time 8.92 x 10^-12 seconds, how far from the origin is the electron?

b.How much time elapses (starting from the instant the electron passes through theorigin) before the z-coordinate of the electron is z = 0 again?

Explanation / Answer

acceleration of electron is in negetive y direction=qE/m=3.51 E14 m/s^2

distance covered in x diection=0

distance covered in y diection=vy*t=5000*8,92 E-12=446 E-10 m

distance covered in z diection=[1000*8.92 E-12]-[0.5 *3.51 E14*(8.92 E-12)^2]=89.2 E-10-1.39 E-10=87.81 E-10 m

total distance=sqrt(446^2+87.81^2) E-10 m=454.56 E-10 m

b) time to return to z=0 t=2u/a=5.68 E-12 sec

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