The origin of an x axis is placed at the center of a nonconducting solid sphere of radius r that carries a charge +qsphere distributed uniformly throughout its volume. a particle that carries an unknown charge qpart is located on the x axis at x=+2r. the magnitude of the electric field due to the sphere-particle combination is zero at x=+r/4 on the xaxis.
part a
what is qpart in terms of qsphere?
express your answer in terms of qsphere.
qpart =
nothing
submitrequest answer
part b
at what other locations on the x axis is the electric field zero?
express your answer in terms of r.
x =
nothing

and

Explanation:

See  attached figure.

E due to sphere

E due to particule

 (1)

according to the law of gauss and superposition Law:

; electric field due to the small sphere with r1=R/4

then:  (2)

on the other hand, for the particule:

  ⇒       (3)

We replace (2) y (3) in (1):

--------------------

if R<x<2R   AND

remember that  

then:

solving:

but: R<x<2R  

so :

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.