Continuous charge distribution Definition and 18 Threads

I sort of understand the meaning of this integral, but I don't know how to evaluate it. I have never evaluated a volume integral. It would be very helpful if someone could explain in other words what this integral means and give an example evaluating it. This is from Purcell's Electricity and...

I'm working through Griffiths EM 3rd ed. in section 2.4.2 (point charge distribution) and 2.4.3 (continuous charge distribution). I understand from the section on point charge distributions that when we add up all the work (excluding the work necessary in creating the charge itself), one clever...

Homework Statement (Taken from Serway and Jewett Chapter 23, Q44, 9th Edition) A thin rod of length ## l ## and uniform charge per unit length ##λ## lies along the x-axis as shown in the image attached. (a) Show that the electric field at P, a distance d from the rod along its perpendicular...

This is my first time using this site so please excuse me if I missed any guidelines. 1. Homework Statement A plastic rod having a uniformly distributed charge Q=-25.6pC has been bent into a circular arc of radius R=3.71cm and central angle ∅=120°. With V=0 at infinity, what is the electric...

Homework Statement This is more of a general question, but a simple example would be find the force on a test charge q at the center of a ring of charge with a total charge Q and a charge distribution given as λ(θ) =ksin(θ) where θ is measured clockwise with respect to the positive x-axis. The...

1. Calculate the work that must be done on charges brought from infinity to charge a spherical shell of radius R = 0.100 m to a total charge of Q = 125 μC.2. V = k_e\int{\frac{dq}{r}} \triangle V = - \int{E \cdot ds} W = q\triangle V 3. I started with assuming the spherical shell produces an...

Homework Statement A nonconducting sphere 1.3 m in diameter with its center on the x axis at x = 4 m carries a uniform volume charge of density ρ = 4.8 µC/m3. Surrounding the sphere is a spherical shell with a diameter of 2.6 m and a uniform surface charge density σ = -1.2 µC/m2. Calculate the...

dE = ke(dq/r2) How to change to complicated equation in the following picture?

I am given a continuous charge problem in which there is a non-conducting wire of legnth L lying along the y-axis and I am required to calculate the electric field at any point along the x-axis. I know how to compute the electric field of a continuous charge distribution at a given point, but...

Homework Statement I am having trouble understanding how \textit{Δ}\vec{E}\textit{ = k}_{e}\frac{Δq}{{r}^{2}} (where ΔE is the electric field of the small piece of charge Δq) turns into \vec{E}\textit{ = k}_{e}\sum_{i}\frac{{Δq}_{i}}{{{r}_{i}}^{2}} then into \vec{E}\textit{ =...

A line of positive charge is formed into a semicircle of radius R = 57.8 cm, as shown in the figure below. (The figure is a semicircle above the x-axis with angle θ measured from positive y axis centred at the origin) The charge per unit length along the semicircle is described by the...

Hello guys, I tried to figure this out and I got my answer. I just want to check it. So would you guys please help me with it? Thank you! Here is the question: A nonconducting rod of length 2a has a charge Q uniformly distributed along it. Find the expression for x-component of the electric...

I'm very sorry for the initial post - I was having trouble working with LaTex (I've never used it before and the preview post wasn't showing me what I had expected it to look like - it kept giving me a square root symbol for every code). Find the electric field a distance z above the centre of...

Why are the integration bounds from -pi/2 to pi/2 and not 0 to pi?

The most general way of calculating the value of the vector electric field at a certain point P is given by the formula E = k times Integral of (dq/r² times unit vector). That means you break the charge distribution into infinitesimal elements dq and vectorially add the contributions of each at...

http://www.vias.org/physics/bk4_06_07.html This is a quote from the mentioned website, " For example, a charged metal ball will have charge spread nearly uniformly all over its surface, and in for most purposes it will make sense to ignore the fact that this uniformity is broken at the atomic...

In the Electric field of a Continuous Charge Distribution, what is "conti.." exactly? -I know its the "distribution"! but I`m asking about, like, how would the "distribution" be continuous? -I think the word "symmetry" should be used? -why is the word "continuous" used?

1. A nonconducting rod of length L = 6cm and uniform linear charge density A = +3.68pC/M . Take V = 0 at infinity. What is V at point P at distance d = 8.0cm along the rod's perpendicular bisector? 2. V = S E * ds One half of the rod = L/2 1/4piEo = 9x10^9 R = sqrt((L/2)^2 +...