Line charge Definition and 87 Threads

Okay so I am a little confused as to where I made a mistake. I couldn't figure out how to program Latex into this website but I attached a file with the work I did and an explanation of my thought process along the way.

TL;DR Summary: Find the electric field of a long line charge at a radial distance where the potential is 24V higher than at a radial distance r_1=3m where E=4V/m. Answer: 29.5V/m. Never mind: I retract this question. The integral apparently is supposed to diverge! I apologize for not reading...

Hi! I think I solved the problem but I would like you to take a look at it please, is it right? is there a better way to solve it?

what I've done so far? -i've determined the vector between the point (4, 0, 0) and the point P. (4, 6, 8) - (4, 0, 0) (0, 6, 8) -The norm of this vector is the radial distance of the line to point P (the value of “ρ” in the formula) √(0^2 + 6^2 + 8^2) = 10 -> ρ = 10 -and its unit vector is...

F = qE ma = (2*10^-6) * (λ / (2pi*r*ε0) ) ma = (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) => I am not certain what to put for r ( But I sub in 4 because dist is 4) a = ( (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) )/ 0.1 a = 0.35950 v^2 = U^2 + 2 a s v = 0 u^2 = -2 a s => Can't sqrt negative so...

Can I sum up the potential due to all positive line charges and all negative line charges separately, with the boundary condition being at the edge of my unit cell, the potential should be the same and inside the metal there is a contant potential?

Homework Statement Find the electric potential of an infinitely long cylinder shell of radius ##R## whose walls are grounded, when in its interior a line charge, parallel to the cylinder, is placed at ##r=a## (with ##a<R##) and that has a lineal charge density ##\lambda##. Homework Equations...

Hey guys, could anyone tell me if set up this integral correctly? Thanks in advanced!

Homework Statement Find an equation for the net electric field at a point, above and between, two infinite line charges, one with line charge density λ and the second with line charge density -λ. The point is a distance R from both line charges, a distance y above the midpoint between charges...

Homework Statement There is a finite line charge with length L = 1 meter and linear charge density λ = 1*10^-16 C/m. Point P is h = 70cm above the line charge and distance x from the right end of the line charge. The magnitude and direction of the electric field at point P must be found. The...

Homework Statement Positive charge Q is distributed uniformly along the x-axis from x = 0 to x = a. Determine a. The electric field produced by the charge distribution Q at points on the positive x-axis where x > a. b. A point charge q is then placed at x = a + r. Determine force on q due to Q...

Homework Statement Two identical thin rods of length L carry the same uniform line charge distribution (charge per unit length) of . If the two rods are collinear (aligned along the same line), with a distance of d between their nearest ends, calculate the Coulomb force (magnitude and...

Homework Statement Find the electric field of an infinitely long straight wire of charge ## \lambda## C/m at a point ##r= ix+jy## Homework Equations ##\int E.da = \frac {Q}{\epsilon_0}## ##E= \frac{\int dq}{4\pi\epsilon_0 r^2} ##r The Attempt at a Solution Drawing a cylindrical gaussian...

Homework Statement A very thin, finite, and uniformly charged line of length 10 m carries a charge of 10 µC/m. Calculate the electric field intensity in a plane bisecting the line at ρ = 5 m. Homework EquationsThe Attempt at a Solution Not sure why I'm not getiting this but I've been at this...

Homework Statement A line charge with uniform charge distribution and linear charge density ##\lambda## lie along z-axis from ##(0,0,-d)## to ##(0,0,+d)##. Find electric field due to this charge along z, x-axis and potential at ##(0,0,2d)##, ##(\sqrt{3}d, 0,0)## and ##(3d/2, 0 , d)##...

Homework Statement Find the Electric field a distance z above one end of a straight line segment of length L that carries a uniform line charge λ Homework Equations Complicated formula due to lack of font for the notation used by the author of the book. so I wrote it out. I did my best to...

Homework Statement A line of charge with a non-uniform charge density lambda=ay, where a=−34.00 nC/m^2 lies along the y axis in the region 0≤y≤2.90 m. Calculate the electric potential of this line of charge at point P on the x axis a distance 0.80 m from the origin. Assume the potential...

1. Homework Statement An infinite line of charge with linear density λ1 = 6.8 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.5 cm and outer radius b = 4.8 cm. The insulating shell is uniformly charged with a volume density of ρ = -667 μC/m3. 1) What is λ2...

Homework Statement Hi everybody! I'm very stuck trying to solve this problem, hopefully some of you can give me a clue about in which direction I should go: Determine the multipole expansion in two dimensions of the potential of a localized charge distribution ##\lambda(\vec{x})## until the...

Homework Statement A long straight wire has a line charge, λ that varies in time according to: λ = λ0e(-βt). A square loop of dimension, a, is adjacent to the wire (at a distance a away from the wire). Calculate expressions for the displacement current at the center of the wire loop and the...

Homework Statement You wish to determine the electric field magnitude along the perpendicular bisector of a 230-mm line along which35 nC of charge is distributed uniformly. You want to get by with a minimal amount of work, so you need to know when it is sufficient to approximate the line of...

Homework Statement I just want to focus on the divergence outside the cylinder (r >R) Homework Equations The Attempt at a Solution For r > R, I said ∇ * E = p/ε But that's wrong. The answer is ∇ * E = 0 I'm confused because there is definitely an electric field outside the cylinder (r...

Homework Statement A long, straight wire has a line charge, λ, that varies in time according to: λ = λ0 exp(-βt). A square wire loop of dimension a is located adjacent to the wire at a distance of a from the wire. Calculate expressions for the displacement current at the center of the wire loop...

Homework Statement https://www.dropbox.com/s/w8xmgdwwqalymm4/000407.png?dl=0 Homework Equations I am not sure. The Attempt at a Solution I really don't understand how to go about this. I really need someone to help walk me through this where I can ask questions along the way. It is not so...

Homework Statement A line charge with a uniform linear charge density Lambda lies along the x-axis and extends from -∞ to 0. Determine the X-component, and Y-component of the E-field at a point P, a distance 'a' from the origin on the positive y-axis. Homework Equations dE= (k*dq/r^2)* r(hat)...

Homework Statement A non conducting rod of length 2.2 m carries a negative charge of 3.8 ×10^-7 spread uniformly over it's length .What is the magnitude of electric field near the mid point of the rod at a perpendicular distance 3.6 mm from the rod? Homework Equations E=λ/2πε0r The Attempt at...

Homework Statement A thin line of charge is on the x-axis from x = -L/2 to L/2. The charge density is non uniform and given by λ = ax where x are the points on the charge distribution. Calculate the electric field for all points along the y axis. Homework Equations E = kQ/r^2 The Attempt at...

Homework Statement We are given a wedge configuration with three sections. There are two conducting planes held at zero potential that make an angle of ##2\beta## with each other. They are connected by a portion of a conducting cylinder with radius ##a##. An infinite uniform line charge of...

Homework Statement Charge is distributed uniformly along an infinite straight line with density λ. Develop the expression for E at the general point P. Homework Equations The electric field at a point P, caused by N point charges Qi, each a distance ri from P, is given by \mathbf{E}...

Homework Statement A non-conducting rod AB, having uniformly distributed positive charge of linear charge density λ is kept in x-y plane. The rod AB is inclined at an angle 30° with +ve Y-axis. The magnitude of electrostatic field at origin due to rod AB is E_0 N/C and its direction is along...

Homework Statement An infinite line of charge with linear density λ1 = 6.2 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.7 cm and outer radius b = 4.4 cm. The insulating shell is uniformly charged with a volume density of ρ = -552 μC/m3.1) What is λ2, the...

Homework Statement A wire at extends for -L to L on the z-axis with charge ##\lambda##. Find the field at points on the xy-plane Homework Equations ##E(r)=k\int\frac{\rho}{r^2}dq## ##k=\frac{1}{4\pi ε_o}## The Attempt at a Solution First time I've looked for field on a plane so I...

Homework Statement Infinite uniform line charges of 5nc/m lie along the (positive and negative) x and y axes in free space. Find E at :P(0,3,4) Homework Equations E due to line charge along the Z-axis is given by: E=(λ/(2∏*ε*r))*ar where λ=line charge density;ε=...

there are 2 rings of charge, radius R on the x-axis separated by a distance R, find the potential and E field. so don't you have to calculate the field to the left of the 2 rings, in between the 2 rings and to the right? I get these answers for the E field which by symmetry points only on the...

Homework Statement Blah Blah irrelevant context.. positively charged plate occupying the x - y plane with charge density ##σ=5.2{\frac{nC}{m^2}}##.This maybe modeled as an infinite charged plane. There is a Charged wire running parallel to the y-axis through the point ##(-2.0cm, 0, 1.0cm)##...

Homework Statement A finite uniform linear charge ρ_L = 4 nC/m lies on the xy plane; start point and end point are (7,0,0) and (0,7,0) .While point charges of 8 nC each are located at (0, 1, 1) and (0, -1, 1). Find E at (0, 0 ,0) Homework Equations dE=ρ_L *dz'/4∏ε *...

This question is a perfect example: A solid sphere 25cm in radius carries 14microC, distributed uniformly throughout it's volume. Find the electric field strength a) 15cm b)25cm and c)50 cm from center. I know that I need my gaussian surface and I also need p=q/v where p is the...

Hello i have some questions about to obtain finite line charge equation. as you know the equation of a finite line charge equation is now i want to demonstrate this equation. at first i assume that charge element on z>0 so 1- i solve the problem but my final answer is different...

Homework Statement A rod lies on the x-axis with one end at the origin and another at x=2. The linear charge density is given by λ(x)=C(x^(3) + 3x^(2)). Find the x-component of the electric field Ex at the origin in terms of q. Homework Equations Ex = ƩdEx ||dE||= (k|dq|/r^(2)) (z/r)...

Homework Statement A line charge starts at x = +x0 and extends to positive infinity. The linear charge density varies inversely with distance from the origin, λ(x)=(λ0*x0)/x derive the expression for the electric field at the origin, E0, due to this infinetly long line-charge (L→+∞)...

Hi, on page 63 of David J. Griffiths' "Introduction to Electrodynamics" he calculates the electric field at a point z above a line charge (with a finite length L) using the electric field in integral form. E_z = \frac{1}{4 \pi \epsilon_0} \int_{0}^{L} \frac{2 \lambda z}{\sqrt{(z^2 + x^2)^3}}...

Homework Statement For the single line charge, derive an expression for Electric Potential. Homework Equations V(r)=-\intE\bulletdr E for infinite line = \frac{\lambda}{2\pi r\epsilon} The Attempt at a Solution The integration is straightforward enough—my question is as to what the...

Homework Statement Find the Electric field at distance z above the mid point of a length L straight line segment, carrying a non-uniform line charge \lambda = \frac{1}{C} |x| where C is a constant 2. The attempt at a solution I note that the horizontal component cancels out...

Homework Statement A line charge in the x directio has a variable charge density given by the equation λ=4 λnot((1-x)/2L), where λnot is a constant. The rod has a length of L. i)What is the net charge of the rod? Hint-the net charge is calculated by integrating the charge density with respect...

Homework Statement This isn't a real HW problem for me but just a question I asked myself and I am slightly confused by the solution I get. Here is the situation. You have an infinite line charge and a point charge q. Find the potential energy given to the point charge from the infinite line...

Homework Statement Pollack, Stump - Electromagnetism. Prob. 9.23 A long straight wire carrying current 1 is parallel to the z axis and passes through the point (a, 0, 0) . The region x > 0 is vacuum, and the region x < 0 is a material with magnetic susceptibility Xm . Show that the...

Homework Statement There is a charge located at the origin of magnitude 5nC. There exists a vertical line of charge, 2 meters in length, that runs from (2m,-1m) to (2m,1m). a) What uniform linear charge density must this line of charge have in order that the net force on a charge placed at...

Homework Statement A uniformly charged, straight filament 7.00 m in length has a total positive charge of 2.00 \muC. An uncharged cardboard cylinder 2.00 cm in length and 10.0 cm in radius surrounds the filament at its center, with the filament as the axis of the cylinder. Using reasonable...

Straight Line Charge of Finite Length (E Field) Homework Statement Find the expression for the E field at an arbitrary point in space due to a straight line of length l uniformly charged with total charge Q. The ambient medium is air. Homework Equations The Attempt at a Solution...