Finding the magnitude and direction in a electric field.

AI Thread Summary
The discussion revolves around calculating the electric field and forces due to three point charges arranged in an equilateral triangle on the X-Y plane. Part A focuses on determining the magnitude and direction of the electric field at the origin, emphasizing the principle of superposition and vector cancellation. Part B addresses the acceleration of an electron placed at the origin, which can be derived from the electric field calculated in Part A. Part C explores whether the acceleration of a proton would differ from that of the electron, concluding that the fundamental principles remain the same due to opposite charges attracting. The thread also includes a separate problem involving the electric field from a uniformly charged spherical surface, with users seeking guidance on integration techniques.
Trap_Shooter
Messages
1
Reaction score
0
Three point charges are placed at the vertices of an equilateral triangle (of side .2m). The triangle is setup on an X-Y plain. On the top of the triangle on the Y-axis the charge is q7= -7μC, the positive X-axis the charge is q3= 3μC, and on the -X-axis the charge is q2= 2μC.

Part A).
What is the magnitude and the direction of the electric field at the origin?

Part B).
What would be the acceleration (magnitude and direction) of an electron placed at the origin?

Part C).
Would the acceleration (magnitude and direction) of the proton be different than that of the electron? Explain.
 
Physics news on Phys.org
As per forum rules, you must post any equations you have that you believe may be relevant and your own attempt at solution, as far as you got.
 
I'm going to parasite on this thread, because it deals with a similar topic.

Problem 2.7 Find the electric field a distance z from the center of a spherical surface of radius R, which carries a uniform charge density δ. Treat the case z < R as well as z > R. Express your answer in terms of the total charge q on the sphere.

the way i approached it was use the electric field equation,

E = \frac{1}{4\piε} \int \frac{1}{|r|^2} \widehat{r}dq

for which i substituted \widehat{r} = cosψ = \frac{z - Rcos\theta}{r} and for |r| = √R^2sin^2θ + (z - Rcosθ)^2 and dq = δda = δr^2sinθdθd\phi

where R is the radius of the sphere upon whos surface the charge is distributed.

Now i substitute all of these wonderful thing into the electric field equation, all giddy to finally solve it :D Integrating over the entire surface of the sphere, that is from 0 to \pi for d\theta and 0 to 2\pi for d\phi

E = \frac{1}{4\piε} \int \frac{1}{ (√R^2sin^2θ + (z - Rcosθ)^2)^2 }\frac{z - Rcos\theta}{(√R^2sin^2θ + (z - Rcosθ)^2)}δr^2sinθdθd\phi

\int d\phi = 2\pi nothing exciting there, parametrize u = cosθ, du = -sinθ dθ

E = \frac{1}{4\piε} \int \frac{δ(2\pi r^2sinθ)(z - Rcos\theta)}{ (√R^2sin^2θ + (z - Rcosθ)^2)^3 }dθ \Rightarrow E = \frac{1}{4\piε} \int \frac{δ(2\pi r^2sinθ)(z - Rcos\theta)}{ (√R^2 + z^2 - 2Rzcosθ)^3 }dθ \Rightarrow E = -\frac{1}{4\piε} \int \frac{δ(2\pi r^2)(z - Ru)}{ (√R^2 + z^2 - 2Rzu)^3 }du

at this point i pretty much just hur dur, try to integrate by partial fractions, and get nowhere because its like no other I've met before.

I realize this is a pretty standard integral, being an inverse cosine law and all. Any online resources?

Would someone please hint as to how to solve this, have i made any mistakes.

attachment.php?attachmentid=55700&stc=1&d=1360733006.gif
 

Attachments

  • sphere.gif
    sphere.gif
    1.4 KB · Views: 689
Last edited:
Trap_Shooter said:
Three point charges are placed at the vertices of an equilateral triangle (of side .2m). The triangle is setup on an X-Y plain. On the top of the triangle on the Y-axis the charge is q7= -7μC, the positive X-axis the charge is q3= 3μC, and on the -X-axis the charge is q2= 2μC.

step one, draw the question. apply principle of superposition; consider one charge at a time, then sum individual forces.

Part A
think about which force vectors are going to cancel at the origin.

Part B
use the result from part A :D

Part C

is pretty vanilla. opposites attract.
 
Thread 'Minimum mass of a block'
Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
TL;DR Summary: Find Electric field due to charges between 2 parallel infinite planes using Gauss law at any point Here's the diagram. We have a uniform p (rho) density of charges between 2 infinite planes in the cartesian coordinates system. I used a cube of thickness a that spans from z=-a/2 to z=a/2 as a Gaussian surface, each side of the cube has area A. I know that the field depends only on z since there is translational invariance in x and y directions because the planes are...
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'
Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is(Figure 2): F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
Back
Top