A) A particle leaves theorigin with a speed of 2 × 106 m/s at 45? to the x axis.

Question

A) A particle leaves theorigin with a speed of 2 × 106 m/s at 45? to the x axis. Itmoves in a constant electric field E = Eyˆj. The charge andmass of an electron are 1.6 × 1019 C and 9.11× 1031 kg and the charge and mass on a proton are1.6×1019 C and 1.67 × 1027 kgrespectively.
Find Ey such that the particle will cross the x axis at x = 3 cm ifthe particle is an electron.

Answer in units of kN/C.

B) Find Ey such that the particle will cross the x axis at x = 3 cmif the particle is a proton.

Answer in units of MN/C. A) A particle leaves theorigin with a speed of 2 × 106 m/s at 45? to the x axis. Itmoves in a constant electric field E = Eyˆj. The charge andmass of an electron are 1.6 × 1019 C and 9.11× 1031 kg and the charge and mass on a proton are1.6×1019 C and 1.67 × 1027 kgrespectively.
Find Ey such that the particle will cross the x axis at x = 3 cm ifthe particle is an electron.

Answer in units of kN/C.

B) Find Ey such that the particle will cross the x axis at x = 3 cmif the particle is a proton.

Answer in units of MN/C.

Explanation / Answer

this goes back to projectile motion equations and combine them withcoulomb force law. F= ma a = F/m Fy = Ey*q ay = Ey*q/m the y position dy is: (1)    dy = v0*t -1/2*ay*t^2 So, according to the problem, you want dy =0 when x = 3 cm. Tosolve for that, you need a time dx = v0x*t (2)   t =dx/(v0*cos(45))          here dx = 3 cm. using (1) and (2) you should be able to solve for acceleration.Once you have ay, you can solve for Ey.

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