1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
FromTheMoon [43]
3 years ago
8

At what distance along the z-axis is the electric field strength a maximum?

Physics
1 answer:
Lesechka [4]3 years ago
4 0
The axial field is the integration of the field from each element of charge around the ring. Because of symmetry, the field is only in the direction of the axis. The field from an element ds in the ring is 

<span>dE = (qs*ds)cos(T)/(4*pi*e0)*(x^2 + R^2) </span>

<span>where x is the distance along the axis from the plane of the ring, R is the radius of the ring, qs is the linear charge density, T is the angle of the field from the x-axis. </span>

<span>However, cos(T) = x/sqrt(x^2 + R^2) </span>

<span>so the equation becomes </span>

<span>dE = (qs*ds)*[x/sqrt(x^2 + R^2)]/(4*pi*e0)*(x^2 + R^2) </span>

<span>dE =[qs*ds/(4*pi*e0)]*x/(x^2 + R^2)^1.5 </span>

<span>Integrating around the ring you get </span>

<span>E = (2*pi*R/4*pi*e0)*x/(x^2 + R^2)^1.5 </span>

<span>E = (R/2*e0)*x*(x^2 + R^2)^-1.5 </span>

<span>we differentiate wrt x, the term R/2*e0 is a constant K, and the derivative is </span>

<span>dE/dx = K*{(x^2 + R^2)^-1.5 +x*[(-1.5)*(x^2 + R^2)^-2.5]*2x} </span>

<span>dE/dx = K*{(x^2 + R^2)^-1.5 - 3*x^2*(x^2 + R^2)^-2.5} </span>

<span>to find the maxima set this = 0, giving </span>

<span>(x^2 + R^2)^-1.5 - 3*x^2*(x^2 + R^2)^-2.5 = 0 </span>

<span>mult both side by (x^2 + R^2)^2.5 to get </span>

<span>(x^2 + R^2) - 3*x^2 = 0 </span>

<span>-2*x^2 + R^2 = 0 </span>

<span>-2*x^2 = -R^2 </span>

<span>x = (+/-)R/sqrt(2) </span>
You might be interested in
A straight wire of length 4.5 cm moves at a constant speed of 5.2m/s perpendicular to its length and a uniform magnetic field. I
liraira [26]
Well you have to minus the 4.5 to 5.2 and the answer to that would be -11.5 and calculated that to be 4.5
3 0
3 years ago
Identify how the energy flows up through the ecosystem. Describe how decomposers help to cycle matter in an ecosystem and their
NNADVOKAT [17]

Answer:

Decomposers are organisms that break down dead or decaying organisms, they carry out decomposition, a process possible by only certain kingdoms, such as fungi. Like herbivores and predators, decomposers are heterotrophic, meaning that they use organic substrates to get their energy, carbon and nutrients for growth and development. While the terms decomposer and detritivore are often interchangeably used, detritivores ingest and digest dead matter internally, while decomposers directly absorb nutrients through external chemical and biological processes. Thus, invertebrates such as earthworms, woodlice, and sea cucumbers are technically detritivores, not decomposers, since they must ingest nutrients - they are unable to absorb them externally.

Explanation:

6 0
2 years ago
University Physics 9.68: Accelerating Compact Disc. A computer disc drive is turned on starting from rest and has constant angul
faust18 [17]

Hey! How are you? My name is Maria, 19 years old. Yesterday broke up with a guy, looking for casual sex.

Write me here and I will give you my phone number - *pofsex.com*

My nickname - Lovely

5 0
3 years ago
I NEED HELP WITH THE QUESTION ABOVEEE
Sergio039 [100]

I think its b if not then I'm sorry buddy:(

3 0
2 years ago
The center of mass of a 0.3 kg (non-uniform) meter stick is located at its 46-cm mark. What is the magnitude of the torque (in N
Sati [7]

Answer:

15cm

Explanation:

7 0
3 years ago
Other questions:
  • A child rides a wagon down a hill. Eventually, the wagon comes to a stop. Which is most responsible for causing the wagon to sto
    13·1 answer
  • What type of particles flow between objects when they are charged by friction or conduction??
    13·1 answer
  • The tenancy of a moving object to continue moving in a strait line or a stationary object to remain in place is called
    13·1 answer
  • What is the weight of a 24.52kg Television dropped on pluto(acceleration of 0.59m/s/s)?
    14·2 answers
  • Where do earthquakes come from?
    6·2 answers
  • Suppose earth's mass increased but earth's diameter didn't change. Describe how the gravitational force between Earth and the ob
    13·1 answer
  • 4
    11·1 answer
  • As rotational speed increases, thrust____?
    10·1 answer
  • How much water makes up earth in percentages? thx?
    9·1 answer
  • Do you think we might have problems with not enough water to supply our needs (water scarcity) in the
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!