An electron and a proton are each moving at 885 km/s in perpendicular paths as s

Question

An electron and a proton are each moving at 885 km/s in perpendicular paths as shown in the following figure. Consider the instant when they are at the positions shown in the figure. (Let d, 3,95 nm and dy 6.00 nm.) Electron Proton (a) Find the magnitude and direction of the total magnetic field they produce at the origin. magnitude 1.300 direction nto the page (b) Find the magnitude and direction of the magnetic field the electron produces at the location of the proton. magnitude 2.29E-4 T direction nto the page (c) Fin the magnitude and direction of the total electrical force and the total magnetic force that the electron exerts on the proton. d magnetic force: magnitude 4.46E-12 X N direction ESeiect electric force: magnitude direction counterclockwise from the +x-axis

Explanation / Answer

(c)

magnitude force Fb = q*v*B*sintheta

theta   = 90

Fb = 1.6*10^-19*885*10^3*2.29*10^-4

Fb = 3.24E-17 N

direction = left along +x axis

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electric force

distance between electron and proton r = sqrt(dx^2+dy^2) = sqrt(3.95^2+6^2) = .18 nm

electric force F = k*e*e/r^2

F = 9*10^9*1.6*10^-19*1.6*10^-19/(7.18*10^-9)^2

F = 4.4E-12 N

direction = 180 - tan^-1(dy/dx) = 123.35 degrees

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part(b)

magnetic field along the axis B = uo*N*I*r^2/(2*(x^2+r^2)^(3/2))

B = 4*pi*10^-7*700*0.38*0.043^2/(2*(0.08^2+0.043^2)^(3/2))

B = 4.125E-4 T <<<<----answer

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