Answer :
Answer:
To make it easier to Understand, consider the circle to be in the usual 3 dimensional x-z plane (the "horizontal plane") and the point of measurement C to be at a distance p (instead of x to avoid confusion with the x-axis) on the y-axis (the "vertical direction").
The answer for a and b is the same. This is because a the horizontal component of a charged portion of a uniform ring is canceled by the opposite portion of the ring since they are placed at an equal distance from the position in which the electric field is being measured or applied, just as are the opposing point charges described in part a.
Explanation:
A.) Using Coulomb's law of point charges, each charge on the circle would exert a field Ec at C given by:
(1) Ec = Ke * (Q / n) / d²
where:
Ke is Coulomb's constant,
Q / n is the magnitude of the charge, and
d = the distance between the charge and the point of measurement C, with d² = a² + c²
Since the charges are in a circle in the x-z plane, all force components in both the x- and the z-directions are canceled by symmetry; the vertical force (that in the y-direction) is the only component that does not cancel.
Therefore the resultant vector Ecy points up (+y-direction) and has a magnitude of:
(2) Ecy = Eq * sin(theta)
= (Ke * (Q / n) / d²) * (c / d)
Then, summing the forces from all the charges, the magnitude of the total electric field is given by:
(3) Ey = n * Ecy
= n * [ (Ke * (Q / n) / d²) * (c / d) ]
= c * Ke * Q / d^3
B.) The equation is the same. This is because both the x- and z-components (the two planar components) of a charged portion of a uniform ring are canceled by the opposite portion of the ring, since they lie at an equal distance but opposite direction from c.
This is the same way the opposing point charges described in part A behave.
Answer:
Check image.
Explanation:
I find this problem has a lack of explanation both here and on Chegg because no one shows the steps of it and it can be confusing. Here's mine to help clear up a bit.
