A dipole is centered at the origin of a coordinate system, and a small charged s

Question

A dipole is centered at the origin of a coordinate system, and a small charged sphere is some distance away along the perpendicular bisector of the dipole. The particle carries a uniformly distributed charge of 3.0 nC, and experiences a 200 nN electric force in the positive y direction. (a) If the dipole charges are ±10 nC and the dipole separation is 20 mm, how far away from the dipole is the sphere? (b) What is the dipole moment vector of the dipole? (c) What is the magnitude and direction of the electric force exerted on the dipole by the sphere? (d) What is the magnitude of the torque exerted on the dipole by the sphere?

Explanation / Answer

a) elctric dipole moment of the dipole, p = q*L

= 10*10^-9*20*10^-3

= 2*10^-10 C.m

eletric field on the equitorail line of the dipole, E = k*p/r^3

force on sphere, F = Q*E

F = Q*k*p/r^3

200*10^-9 = 3*10^-9*9*10^9*2*10^-10/r^3

==> r = 0.3 m <<<<<<-------------Answer

b) p = 2*10^-10 j C.m (toards +y axis)

c) magnitude of force = 200 nN <<<<<<-------------Answer

direction : towards -y axis. <<<<<<-------------Answer

d) torque = E cross p

= k*Q/r^2*p*sin(90)

= 9*10^9*3*10^-9/(0.3^2)*2*10^-10

= 6.0*10^-8 N.m <<<<<<-------------Answer

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