An electron is at the coordinate (x,y) = (0,1) nm. A proton is at the coordinate

Question

An electron is at the coordinate (x,y) = (0,1) nm. A proton is at the coordinate (x,y) = (0,-1) nm.

(a) What is the force that these two particles exert on a proton at location (x,y) = (1,0) nm? What is the force that these two particles exert on an electron at location (x,y) = (1,0) nm?

(b) What is the force that these two particles exert on a helium nucleus at location (x,y) = (1,0) nm?

(c) What is the force that these two particles exert on a neon nucleus at location (x,y) = (1,0) nm?

(d) What is the force that these two particles exert on a xenon nucleus at location (x,y) = (1,0) nm?

detailed answer please. I'm trying to really learn this.

Explanation / Answer

r = sqrt(1^2+1^2) = sqrt2 nm

electric field due to electron

E1x = -k*q*costheta/r^2 = -(9*10^9*1.6*10^-19*cos45)/(2*10^-18) = -509116882.45 N/C

E1y = k*q*sintheta/r^2 = (9*10^9*1.6*10^-19*sin45)/(2*10^-18) = 509116882.45 N/C

electric field due to proton

E2x = k*q*costheta/r^2 = (9*10^9*1.6*10^-19*cos45)/(2*10^-18) = 509116882.45 N/C

E2y = k*q*sintheta/r^2 = (9*10^9*1.6*10^-19*cos45)/(2*10^-18) = 509116882.45 N/C

net electric field due to electron and proton

Ex = E1x + E2x = 0

Ey = E1y + E2y = 1018233764.9 N/C

(a)

F = E*Q = 1018233764.9*1.6*10^-19 = 1.63*10^-10 N

(b)

F = E*Q = 1018233764.9*1.6*10^-19 = 1.63*10^-10 N

(c)

Q = 0

F = 0

(D)

Q = 0

F = 0

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