Electric field Definition and 1000 Threads

For a fixed point in space, the first-order electric field correlation function may be given as (Possibly incorrectly, see my "second" post to this thread)! $$\langle\vec E^*(t)\vec E(t+\tau)\rangle = {\frac {1} {T}} \int_T\vec E^*(t)\vec E(t+\tau)dt~~~~~(1)$$ Where T is a very large time and *...

Homework Statement In a lab experiment we measured the potential at different points within a cylindrical capacitor electric field modeling plate thing (apparently that's the best I could do to translate that into English). The positive electrode was connected in the middle and the negative...

Homework Statement [/B] Here's the problem from the homework. I've called the initial positions in order as 0, l, and 2l. Homework Equations The most important equation here would have to be |V - w2*M| = 0, where V is the matrix detailing the potential of the system and M as the "masses" of...

Imagine that I have a straight, statically-charged, cylinder-shaped tube with arbitrary (ideally infinite) extent. The charge is distributed evenly over the tube such that the field inside the tube is zero. For convenience, let's line up the tube centered along the x-axis such that the...

I have what at first seems like a very simple problem, yet I have no clue how to solve it. There is 1 point defined to have 0V, and another point has exactly 1V. Assume there is nothing else in the universe. https://i.imgur.com/iv9oL5j.png How do I find the electric potential and field at any...

Homework Statement This is irodov's problem #310 in electrodynamics A long solenoid of cross-sectional radius a has a thin insulated wire ring tightly put on its winding; one half of the ring has the resistance ## \beta ## times that of the other half. The magnetic induction produced by the...

Homework Statement This was a one mark question on an AS paper. [/B]Homework Equations [/B]The Attempt at a Solution Mark scheme says straight lines, equally spaced lines pointing down and starting/ending on the plates. (which I totally get if one plate was 0V or negative) However, if you...

Homework Statement Given 2 positively charged parallel plates with equal surface charge densities, calculate the electric field at a point outside the the parallel plates. Homework Equations E= (surface charge density) / 2(relative permittivity) for a single sheet. The Attempt at a Solution...

Is it a magnetic or an electric field that causes induction in the antenna wiki says that: The electric field (E, green arrows) of the incoming wave pushes the electrons in the rods back and forth, charging the ends alternately positive (+) and negative (−). enter image description here...

Homework Statement The figure below shows a spherical shell with uniform volume charge density ρ = 1.87 nC/m3, inner radius a = 15.0 cm, and outer radius b = 2.60a. [Reference Picture] What is the magnitude of the electric field at the following radial distances? Homework Equations...

Hi. I know how to use Gauss' Law to find the electric field in- and outside a homogeneously charged sphere. But say I wanted to compute this directly via integration, how would I evaluate the integral...

Homework Statement No variables, just a conceptual question. Homework Equations Flux = EA = Q/ε The Attempt at a Solution Given a uniformly charged rod of FINITE length, could we use Gauss' law for electric flux to calculate the field at a point p a distance x away from the rod, so long as the...

Homework Statement Given electric field ##\vec E = 6x^2\hat i +6y\hat j+4\hat z## v/m Find ## V_{MN}## if both M and N separate by M(2,6,-1) and N(-3,-3,2) Homework Equations The Attempt at a Solution here i find ##V_{MN}## by unit vector from N to M is ##\frac 1 {\sqrt (115)}(5\hat i +9\hat...

The Magnetic Dipole Moment for a Magnetic Field for a dipole oriented on the x-y axis is: ##\bar m = |m| \hat z## The Magnetic Field is: ##\bar B = \frac{\mhu_0}{4 * \pi * |\bar r|^5} * 3 * \bar r * (\bar m . \bar r) - \bar m * |\bar r|^2## Vector Potential is: ##\bar A = \frac{\mhu_0}{4 * \pi...

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 https://imgur.com/a/wpir4 [/B] a. What is the strength of the electric field at the position indicated by the dot in the figure? Use the following values: q1 = 1.09 nC, q2=0.93 nC, d1=2.49 cm, d2=6.9 cm, d3 = 4.27 cm. b. What is the direction of the electric field at the...

Ok, this might be a really dumb question, but I still am asking it: I was reading about gauss' Law when it comes to a hollow conductor with a (say) point charge inside it, and it seems intuitive to me that, in electrostatic equilibrium, the charges rearrange themselves to cancel the electric...

Homework Statement Figure 23-30 shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 µC/m2 on its outer surface and radius 3.0 cm. Shell 2 has uniform surface charge density -3.8 µC/m2 on its outer surface and radius 2.0 cm. The shell centers...

Homework Statement I've seen many books writing the cosine rule like this: a^2 = b^2 + c^2 - 2bc cos A My electricity textbook for an electric field in a point between two charges says this: E resultant = root[E1^2 + E2^2 + 2*E1*E2*cos(angle between E1 and E2)] In the first equation it is -2...

Homework Statement What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of 1.50×104 V? Homework Equations ΔV = qΔU ΔV = -∫E⋅dl E = kq/r2 The Attempt at a Solution I am not sure where to...

Hi, I recently came across the familiar image of a metal sphere in an electric field: https://i.stack.imgur.com/x58Ia.jpg I noted how the free-charges on the surface of the sphere align with the electric field lines as opposite charges are attracted. Then I wondered, 'what if the sphere was...

Homework Statement Consider an equilateral triangle of side 15.6cm. A charge of +2.0μC is placed at one vertex and charges -4μC each are placed at the two. Determine the electric field at the centre of the triangle. Homework Equations E=kQ/r^2 The Attempt at a Solution I am hoping someone...

I looked through this forum post for an answer to my problem. It gave me enough insight to try and come to some conclusions but I'm still confused on some parts here and there about how I got my final answer. 1. Homework Statement A uniformly charged, straight filament 7.70 m in length has a...

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 https://imgur.com/gallery/YwCap In side are image of figure, and questions.Homework Equations E = kq/r^2 The Attempt at a Solution So I have an electric field where the y compontents cancel. I have 2Ecos(∂) = E (Electric field at point A) - 2 because there is a top and...

This is from a lab where my team found the equipotential lines from the electric field of a dipole. The information I was given to calculate the magnitude of the electric field seems too simple, and for some reason I'm expecting this to be more complex. So, this is my attempt at double checking...

Could anyone please let me know if breakthrough spark can happen, or, in general, what will happen in the below system? Note 1: the dielectric layers have a much higher breakthrough voltage than humid air. Note 2: the intensity of the electric field that develops in the flow of the humid air is...

I want to calculate Electric field inside and outside a capacitor(two parallel conductor plates and in between a dielectric) which is fed by an AC voltage source. My problem is I do not know how can I relate the electric field to the potential in a capacitor. I got confused about the derivative...

Hi guys, I was reading about electromagnetism, specifically about the application of Gauss' Law to an infinite charged sheet, and how its electric field doesn't depend on the distance from the sheet. I think I have finally managed to wrap my mind around the concept intuitively, based on one of...

Hi guys! I was wondering about the relation between the Gradient, Electric Potential, and Electric Field. I know that if you take the Gradient of a scalar field, you get a resultant vector field in which the vector points in the direction of greatest increase when you take a infinitesimally...

Homework Statement A sphere with a charge of -3.5 x 10^-9 C and a radius of 1.0x10^-2 m is located at the origin of a coordinate system. What is the electric field 1.75 x 10^-2 m away from the center of the sphere along the positive y axis? Homework Equations e = kQ/r^2 The Attempt at a...

Homework Statement The electric field at 2 cm from the center of long copper rod of radius 1 cm has a magnitude ##3 \frac{N}{C}## and directed outward from the axis of the rod. (a) How much charge per unit length exists on the copper rod? (b) What would be the electric flux through a cube of...

Hi people, I was reading on my textbook on electromagnetism (Halliday) about using integral to field the electric field of a charged ring (1D) at a point P located on an axis perpendicular to the ring's plane. The ring is uniformly charged. The book (and my professor) both breakdown each element...

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 There is a large positively charged plate whose charge density is ##\sigma = 2.0 × 10^{-5}\frac{C}{m^2}##. What is the electric field at a point P, that is not enclosed between the plates. Homework Equations For an infinite sheet: $$\vec E = \frac{\sigma}{2\varepsilon_0}\hat...

Homework Statement Taken from Purcell Problem 1.33 Consider the electric field of two protons a distance b apart. The potential energy of the system ought to be given by U=∫E2dv. Let E1 be the field of one particle alone and E2 that of the other. Evaluate ε0∫E1⋅E2dv. Set one of the protons...

Homework Statement From a distance of 10 cm, a proton is projected with a speed of ##v = 4.0 × 106 \frac{m}{s}## directly at a large, positively charged plate whose charge density is ##\sigma = 2.0 × 10^{-5} \frac{C}{m^2}##. (See below.) (a) Does the proton reach the plate? (b) If not, how far...

Homework Statement A proton is at the origin and an ion is at x1 = 6 nm If the electric field is zero at x2 = -3 nm , what is the charge on the ion? Homework Equations for ion The Attempt at a Solution https://imgur.com/ryyuQBq I just have used all my attempts besides one. So I...

Homework Statement Two thin conducting plates, each 25.0 cm on a side, are situated parallel to one another and 5.0 mm apart. If ##10^{-11}## electrons are moved from one plate to the other, what is the electric field between the plates?Homework Equations $$\vec E(P) = \frac{1}{4\pi...

Homework Statement A uniformly magnetized and conducting sphere of radius R and total magnetic moment m = 4\pi MR^3/3 rotates about its magnetization axis with angular speed \omega. In the steady state no current flows in the conductor. The motion is nonrelativistic; the sphere has no excess...

I'm confused as to how this expression E= (δ/εo) can't be used to calculate the electric field of a perfectly flat part of a surface even farther from just above the surface.If you just extend the same cylindrical Gaussian surface used for this proof, wouldn't the field stay the same no matter...

Homework Statement In the layer ##0<z<a## there is a uniform and constant density of charge ##\rho>0##. In the layer ##-a<z<0## the density of charge is ##\rho<0##. What is the total electric field in the space?The Attempt at a Solution By the Gauss law I find that if ##z \geq a## or ##z \leq...

Homework Statement Two positively charged metal spheres are suspended from the same hook by light strings of equal length, making an angle of 10.0◦ with each other. The charges carried by the spheres are as shown in the diagram. After that, the spheres are brought in contact briefly, then...

Homework Statement A ionized gas (overall neutral) is in a cylindrical box with radius ##R## and ##h<<R##, with is main axis along ##\hat{z}## (there is acceleration of gravity ##\vec{g}=-g \hat{z}##). The ions are points: some of mass ##M## and charge ##q>0## (heavy positive ions) and some of...

Suppose we have an energized conductor say 10m above the ground, my understanding is that E Field at the ground will be 0 v/m. My question is, if we have say 8m tall steel tower approximately 3m from the energized conductor and grounded. What is the electrical field on this grounded steel...

<Moderator's note: Moved from a technical forum and therefore no template.> Hi, I've been doing this excersice but I'm not quite sure about my answer It says: A positive charge Q is located at the origin of a three-dimensional coordinate system. Consider and imaginary square surface of side...

This Wikipedia article https://en.m.wikipedia.org/wiki/Relativistic_electromagnetism seems (to me) imply that there is always a frame of reference in which a magnetic field can be rather viewed as an electric field modified by relativistic considerations. Is that always true? That is...

Hi I'm running an experiment where I want to see the electrical field generated when I energise a submerged anode (an array consisting of 4 x stainless steel tubes spaced equidistance apart) and cathode array (similar to the anode) upstream and downstream of the flowing water tank (glass sided...

1. The problem statement "If charges are free to move, the field lines will straighten and shorten as the charges move together" 2. Questions in relation to statement Are there any cases in which charges aren't free to move between two charged objects such as between conductors or insulators...

Homework EquationsThe Attempt at a Solution A)[/B] In the spherical cavity, let me have a Gaussian Spherical Surface around the center. Applying Gauss' s Law for dielectrics, ##\oint _S\vec D⋅ d \vec a = Q_{f_{en}} ## Due to the symmetry of the problem and ## Q_{f_{en}} =0## , ## \vec D = 0...