A dipole is centered at the origin and is composed of charged particles with cha

Question

A dipole is centered at the origin and is composed of charged particles with charge +4e and 4e, separated by a distance 9 1010 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, 8 108, 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 (8 108, 0, 0) m. What is the force on the electron due to the dipole? (Express your answer in vector form.)

Explanation / Answer

(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, 8 108, 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 (8 108, 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

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