Question

The electric field of a uniformly charged ring centered at the origin and laying on the xy plane is given by

E = (Q/4πε0)[ z/(z ^{2} + a ^{2})^{3/2}]
ˆk,

where a is the radius of the ring and Q is its total charge.

Show that a small test charge −q (q > 0) with mass m will undergo simple harmonic motion with an angular frequency

ω = [qQ/4πε0ma^{3} ]^{1/2}

for |z|<< a.

Answer #1

Electric Field of a Charged Sphere with a small hole on the
surface.
Consider a spherical shell of radius R centered on the origin of
coordinates. The sphere is uniformly charged, with total charge Q,
except for the region where theta <= 1.00?. Consider field point
on the positive z-axis. Determine E as a function of z.

A ring of charge with radius R = 1.5 m is centered on the origin
in the x-y plane. A positive point charge is located at the
following coordinates: x = -10.1 m y = 16.8 m z = 17.1 m The point
charge and the total charge on the ring are the same, Q = +22 C.
Find the net electric field along the z-axis at z = 1.6 m.
Enet x=?
Enet y=?
Enet z=?
Thanks!!

3)
A thin ring made of uniformly charged insulating material has total
charge Q and radius R. The ring is positioned along the x-y plane
of a 3d coordinate system such that the center of the ring is at
the origin of the coordinate system. (a) Determine an expression
for the potential at an arbitrary location along the z-axis in
terms of Q, R, and z. (b) Use this expression to determine an
expression for the magnitude of the electric...

A circular ring of charge, with radius R,is placed in the
xy-plane and centered on the origin. The linear charge density of
the ring isλ=λ_o*cos^2(φ), where φ is the cylindrical polar
coordinate such that any point in space is indicated by (r, φ, z).
Find the electric potential anywhere on the z-axis as a function of
z . Using this electric potential find the electric field anywhere
on the z-axis also as a function of z

The electric field on the axis of a uniformly charged ring has
magnitude 360 kN/C at a point 6.6 cm from the ring center. The
magnitude 16 cm from the center is 150 kN/C ; in both cases the
field points away from the ring.
A) What is the Radius of the ring?
B) What is the charge of the ring?
Please show your work

The electric field in a point on the central axis of a uniformly
charged very thin ring is given by the expression:
E = (k*lambda*2pi*R)/((x^2 +R^2)^(3/2)) i cap
where R is the radius of the ring, lambda is the linear charge
density, and x is the distance of the point on the central axis to
the center of the ring. Use this expression (do not derive it!) to
calculate the field in a point inside a thin shell with uniform...

The x component of the electric field, at the origin of an xy
plane, if there is a 0.4 C charge at position (-2, -3) and a 0.2 C
charge at position (1, -3) is _____ N / C
The y component of the electric field, at the origin of an xy
plane, if there is a 0.4 C charge at position (-2, -3) and a 0.2 C
charge at position (1, -3) is _____ N / C

A certain uniformly-charged ring has a radius of 24.0 cm and the
electric potential (relative to points very far away) at its center
is 382 V. What is the electric potential on its axis 18.0 cm from
the plane of the ring?
options:
a) 197 V
b) 287 V
c) 306 V
d) 364 V
e) 219 V

A thin ring of radius R in the x − y plane is centered at the
coordinate origin, and is charged with linear charge density λ
which depends on the polar angle θ as λ(θ) = λ0 sin(θ), where λ0
> 0.
(a) Sketch λ(θ) for θ ∈ [0, 2π].
(b) Before doing any calculations, sketch the E~ x and E~ y
vector components of the electric field at the coordinate origin,
as well as where (roughly) you expect the...

Total charge q2 is uniformly placed on a ring of radius R. The
magnitude of the electric field at position z on the axis of the
ring is given by ((kq2z)/(R^2+z^2)^(3/2))
A uniformly charged rod of total charge q1 and length L is now
placed on the z axis. The nearest end of the rod is at distance L
from the center of the ring, i.e. the rod extends from z = L to z =
2L (see figure on...

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