Question

A dipole is centered at the origin and is composed of charged particles with charge +4e and −4e, separated by a distance 9 ✕ 10−10 m along the y axis. The +4e charge is on the −y axis, and the −4e charge is on the +y axis. (Hint: Make a diagram. One approach is to calculate magnitudes, and get directions from your diagram.)

(a) A proton is located at (0, 8 ✕ 10−8, 0) m. What is the force on the proton due to the dipole? (Express your answer in vector form.)

(b) An electron is located at (−8 ✕ 10−8, 0, 0) m. What is the force on the electron due to the dipole? (Express your answer in vector form.)

Answer 1

(a)

Given that,

q = 4e

distance b/w two charges, d = 9*10^(-10) m

r = 8*10^(-8) m

Dipole moment, P = q*d = 4*1.6*10^(-19)*9*10^(-10)

P = 57.6*10^(-29) Cm

At (0, 8 ✕ 10−8, 0) m,

Electric field due to this dipole (axial),

E = 2kP / r^3

E = 2*9*10^9* 57.6*10^(-29) / (8*10^(-8))^3

E = 2.025*10^4 N/C

force on the proton ,

F = qE

F = 1.6*10^(-19)*2.025*10^4

F = 3.24*10^(-15) (-j) N

(b)

At (−8 ✕ 10−8, 0, 0) m

Electric field due to this bipole (perpendicular),

E = kP / r^3

E = 9*10^9* 57.6*10^(-29) / (8*10^(-8))^3

E = 1.012*10^4 N/C

force on the proton ,

F = qE

F = 1.6*10^(-19)*1.012*10^4

F = 1.62*10^(-15) (-j) N