Answer to Question #231927 in Physics for Mosses07

Question #231927

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 charge is 10 nC and the dipole separation is 20 mm, how far away from the dipole is the sphere?

(b) How is the dipole moment oriented?


1
Expert's answer
2021-09-03T08:25:01-0400

Find the distance from the dipole ends to the sphere:


D2=a2+x2D^2=a^2+x^2

The force between the green and blue charge and the sphere:


F1=kqQD2=kqQa2+x2. F2=kqQD2=kqQa2+x2.F_1=k\frac{qQ}{D^2}=k\frac{qQ}{a^2+x^2}.\\\space\\ F_2=k\frac{qQ}{D^2}=k\frac{qQ}{a^2+x^2}.

The sine of the angle between the x-axis and the forces is


sinθ=aD=ax2+a2.\sin\theta=\frac{a}{D}=\frac{a}{\sqrt{x^2+a^2}}.

The resultant of 200 nN is


R=F1sinθ+F2sinθ= =2kqQa2+x2ax2+a2=2kaqQ(a2+x2)32.R=F_1\sin\theta+F_2\sin\theta=\\\space\\ =\frac{2kqQ}{a^2+x^2}·\frac{a}{\sqrt{x^2+a^2}}=\frac{2kaqQ}{(a^2+x^2)^{\frac32}}.

Solve this equation using any method you prefer (I used Wolframalpha.com), the distance is


a=0.3 m.a=0.3\text{ m}.

As we see, the moment is oriented clockwise.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment