What is Induced charge: Definition and 47 Discussions

Induced-charge electrokinetics in physics is the electrically driven fluid flow and particle motion in a liquid electrolyte. Consider a metal particle (which is neutrally charged but electrically conducting) in contact with an aqueous solution in a chamber/channel. If different voltages apply to the end of this chamber/channel, electric field will generate in this chamber/channel. This applied electric field passes through this metal particle and causes the free charges inside the particle migrate under the skin of particle. As a result of this migration, the negative charges moves to the side which is close to the positive (or higher) voltage while the positive charges moves to the opposite side of the particle. These charges under the skin of conducting particle attract the counter-ions of the aqueous solution; thus, the electric double layer (EDL) forms around the particle. The EDL sing on the surface of the conducting particle changes from positive to negative and the distribution of the charges varies along the particle geometry. Due to these variations, the EDL is non-uniform and has different sings. Thus, the induced zeta potential around the particle, and consequently slip velocity on the surface of the particle, vary as a function of local electric field. Differences in magnitude and direction of slip velocity on the surface of the conducting particle effects the flow pattern around this particle and causes micro vortices. Yasaman Daghighi and Dongqing Li, for the first time, experimentally illustrated these induced vortices around a 1.2mm diameter carbon-steel sphere under the 40V/cm direct current (DC) external electric filed.
Chenhui Peng et al. also experimentally showed the patterns of electro-osmotic flow around an Au sphere when alternating current (AC) is involved (E=10mV/μm, f=1 kHz).
Electrokinetics here refers to a branch of science related to the motion and reaction of charged particles to the applied electric filed and its effects on its environment. It is sometimes referred as non-linear electrokinetic phenomena as well.

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  1. haruspex

    B Symmetry regarding induced potentials?

    A homework thread, https://www.physicsforums.com/threads/point-charge-with-very-thin-metal-sheet-along-a-spherical-surface.1057702/, references https://arxiv.org/pdf/1007.2175.pdf. There is an uncharged conductor and a point charge. In the paper referenced, ##\bar\phi_y(x)## is defined as the...
  2. A

    I Why is there no induced charge outside of the conductor?

    If we put a positive charge outside of a conductor, there is an induced charge, but if we put a positive and negative charge inside a conductor, there is no induced charge?
  3. patric44

    Confirming the dimension of induced charge density of a dielectric

    hi guys our professor asked us to confirm the units of volume charge density ρ and also the surface charge density σ of a dielectric material given by $$ \rho = \frac{-1}{4\pi k} \vec{E}\cdot\;grad(k) $$ $$ \sigma= \frac{-(k-1)}{4\pi} \vec{E_{1}}\cdot\;\vec{n} $$ I am somehow confused about the...
  4. RodolfoM

    How Do Induced Charges Affect Conductors in Electrostatic Fields?

    My first attempt at solving this was to calculate the induced charge in A by making ##V=0##: ##\frac{q_{A}}{4πεR_{1}}+\frac{q_{B}}{4πεR_{3}}=0## ##q_{A}=-q_{B}\frac{R_{1}}{R_{3}}## But that's not the answer. Any help is welcome!
  5. Kaguro

    Induced charge density at the interface of dielectric slabs

    E0=V/d = 100/0.1 =1000v/m In slab 1, E1=E0/k1=500v/m In slab 2, E2=E0/k2=250v/m Applying Gauss' Law to a box surface surrounding the interface with area equal to the plates we have (-E1+E2)*A = Q/epsilon_naught So charge density sigma = -250 epsilon_naught But answer given is...
  6. T

    Capacitance and induced charge of a spherical Capacitor + dielectric

    I) For the first part I used: ##V = - \int E ds = \int_a^c \frac{1}{4\pi\epsilon_0} Q /r^2 dr+ \int_c^{c+d} \frac{1}{k} \frac{1}{4\pi\epsilon_0} Q /r^2 dr + \int_{c+d}^b \frac{1}{4\pi\epsilon_0} Q /r^2 dr ## And by using ##C = Q/V## We get an answer which is somehow large for writing here...
  7. K

    How Does a Dielectric Influence Charge Induction on a Conducting Shell?

    Homework Statement Imagine having a conducting sphere with free charge ##Q## surrounded by a spherical shell filled with a dielectric and then a conducting spherical shell with no free net charge. I want to find out the charge induced on the spherical conducting shell by the sphere or by the...
  8. Rakesh Kumar Jaiswal

    Charge induced on parallel plates if a charge between plates

    Two infinite conducting plates 1 and 2 are separated by a distance l. A point charge q is located between the plates at a distance x from plate 1. Find the charges induced on each plate. Many of the places this problem has been solved by considering an infinitely large plate in place of the...
  9. Kaguro

    Induced charge in image problem

    Homework Statement Find induced charge density in the classic image problem. Sorry, I uploaded my work in form of an image instead of typing. I have tried to use polar coordinates to solve this. But i must have done something wrong. Please help me find the mistake.
  10. Raihan amin

    Induced surface charge distribution

    Two identical metalic spherical conductor of radii ##R## are at a distance ##d## apart.One of the conductor has charge ##Q## while the another one is neutral.What will be the induced charge on the other conductor ? If we put an image charge ##q## inside the neutral one. Then the potential at...
  11. M

    What Causes Discrepancies in Calculating Induced Charge Ratios?

    Dear colleagues I have this problem which I don't understand from where they got the solution I tried to solve it with slot of methods with the same answer which not the stated answer. A point charge (q) is located a distance (b) from a grounded conducting sphere with radius (a) show that the...
  12. mertcan

    Induced charge density -- non-zero potential case

    Hi, Let's think 2 arbitrary shape conductors with non zero charged. If these 2 conductors are closed, there will be induced charge density over surfaces of these conductors. I have not seen such an example, instead there are lots of problems which involve zero(grounded) potential case and...
  13. doktorwho

    Calculate the induced charge on a conducting surface

    Homework Statement A very thin plane of length ##2a## is placed in the air at height ##a## above the conducting surface. The plane is charged on its surface and the expression for it's surface charge density (##ρ_s##) is given by ##ρ_s=ρ_{s0}*\frac{x}{a}## and ##ρ_{s0}## is some constant. a)...
  14. M

    Induced Charge on a Grounded Sphere

    Homework Statement A point charge q is located a distance d away from the centre of a grounded conducting sphere of radius R<d. I need to find the charge density on the sphere and the total induced charge on the sphere. This is very similar to example 2 here...
  15. DrPapper

    Potential of a Rectangular Pipe by Laplace's Equation

    Homework Statement Homework Equations Is my part a correct and am I on the right track for part b? If not please give me some suggestions to get me closer to the right track. Also, how would I even begin c.? We have literally done no examples like this in class. The Attempt at a Solution...
  16. Titan97

    Derivation of induced charge on a dielectric

    Homework Statement Show the the induced charge density on a dielectric placed inside a capacitor is given by $$\frac{k-1}{k}\sigma$$ where ##\sigma## is the charge density of the capacitor plates and ##k## is the dielectric constant. Homework Equations $$E=\frac{E_0}{k}$$ The Attempt at a...
  17. V

    No. of Electrons on Hard Disks: New vs Used

    Is the no. of electrons on a brand new unused and untested harddisk is different from no. of electrons on a used hard disk completely filled with data. i mean will there be even a change of one electron? Please consider the following points before answering: 1- Does all the electrons from a...
  18. S

    Find induced charge on conducting cube in uniform field

    Problem statement, equations, and work done: A perfectly conducting cube is placed in a uniform electric field in the x direction (see attached). Step1 : Use Gauss's law to determine the electric field inside the cube.##\phi_E = 2E(r)A = \frac{q}{\epsilon_0} →...
  19. P

    (Challenging) Conceptual Question on Induced Charge on Conductor

    Here is the question that we have been debating for the past day or so: Take a conducting cubic box and center a conducting sphere with charge +q inside of it. Will the induced charge density on the sphere be uniform or not?My gut instinct is no. The cube and sphere have different symmetries...
  20. S

    Induced charge density problem

    Homework Statement I actually have three problems that have one thing in common that I don't understand. I will try to shortly describe all of them: 1. We have two perpendicular planes. (See Attachment: sketch1.png) The idea is to describe the electric potential in space. Now you can believe...
  21. C

    Induced Charge on a Conducting Disk

    Homework Statement A large, thin plastic disk with radius R = 1.1 meter carries a uniformly distributed charge of Q = -7e–5 C. A circular piece of aluminum foil is placed d = 3 mm from the disk, parallel to the disk. The foil has a radius of r = 6 cm and a thickness t = 1 millimeter. a. Find...
  22. S

    Induced Charge Density on Sheet of Metal

    Homework Statement A charge is located a distance 'a' above a sheet of metal. The charge density induced on the sheet of metal is (-2aQ)/(4pi(ρ^2+a^2)^(3/2)). Since there are no dimensions indicated for this plate, would it be plausible to assume that we are integrating from zero to...
  23. T

    Laser induced charge in glass?

    i am just being curious about some details about how laser can induce charges inside a glass bulk? Does anyone else have more knowledge on this?
  24. V

    Simple doubt in induced charge

    When a positive point charge q is brought close to a neutral conducting spherical shell then negative charges will be induced on the part of the shell closer to q and equal positive charges will appear on side of the shell farther from q.I understand this part. But if the conducting spherical...
  25. L

    Induced charge on a solid metal sphere

    All I understand clearly that if a metal sphere is charged then the charges must reside on the surface because that is the only way there is no electric field within the metal. However if you imagine a neutral metal sphere, and let's say it is suddenly enclosed by a uniformly charged metal...
  26. fluidistic

    Understanding the physics of induced charge over a perfect conductor

    Understanding the physics of "induced charge" over a perfect conductor When we put a perfect conductor, let's say a sphere inside an external electric field, there will be a surface charge distribution different from 0 even though the sphere is electrically neutral. I don't really understand...
  27. mishima

    How does induced charge affect the balance of a conducting beam?

    Say you had a rectangular piece of conductor perfectly balanced on a central pivot point. Around it, you put something that causes an electric field throughout the region. On one end of the balanced piece, atomic cores get exposed as the electron sea rushes to the opposite side via induction...
  28. M

    Introduction to Electrodynamics: External Field & Induced Charge

    Homework Statement Introduction to Electrodynamics by Griffiths, 3rd ed. pg 141-2, Example 3.8: An uncharged metal sphere of radius R is placed in an otherwise uniform electric field E=(0,0,E). [The field will push positive charge to the northern surface of the sphere, leaving a negative...
  29. 1

    If a conductor gets an induced charge is then grounded

    If a neutral conductor gets an induced charge and is then grounded, will electrons from the ground flow into the conductors induced positively charged side, resulting in a net negative charge for the whole conductor?
  30. P

    How Does a Point Charge Affect Induced Charges on Grounded Infinite Plates?

    Homework Statement two infinite conducting plates 1 and 2(both grounded or connected by a wire so that their potential is same) are separated by a distance l. A point charge q is located between the plates at a distance x from plate 1. find the charges induced on each plate. Homework...
  31. A

    What Is the Correct Induced Charge on an Uncharged Conductor?

    The question itself is easy. E field at 2 is zero. E field at other points are of magnitude \frac{\eta}{2\epsilon} But I am arguing with my classmate and tutor that what is the charge induced on the uncharged conductor. For me, I simply use the rule induced charge (charge of same magnitude...
  32. W

    How does induced charge separation work and why can it be confusing?

    Homework Statement I am having trouble understanding the concept of induced charge separation. In my textbook, there is a diagram that demonstrates the procedure, but it gets confusing because the first image is normal, and then it gets inverted? I don't understand in the second set-up if it...
  33. D

    A question on induced charge

    A positive charge Q is located at a distance L above an infinite grounded conducting plane. What is the total charge induced on the plane? (A) 2Q (B) Q (C) 0 (D) -Q (E) -2Q I know the answer is C, but why? Thanks a lot!
  34. Z

    Finding Final Flux in a Flat Coil-Ring System

    Homework Statement A flat coil of area A and n turns is placed at the centre of a ring of radius r(r2>>A) and resistance R. The two are coplanar. When current in the coil increases from 0 to i, the total charge circulating in the ring is? The Attempt at a Solution dQ=dΦ/R Initial...
  35. F

    Induced charge on a conductive shell, potential theory

    There's no electric field inside a conductor, a classic observation of electrostatics. Any field that "should" exist is compensated for by charge redistribution on the surface of the conductor. This produces classic results like shielding since in a hollow conductive shell, the field is still...
  36. K

    Induced charge on plates of capacitor

    Homework Statement Two large plane conducting plates are connected by a wire and are a distance D apart in a vacuum. A point charge +q is placed in the space between them, and at a distance b(<D) from one of them. What proportion of charge q is induced in each plate? Homework Equations...
  37. A

    Induced charge in conducting plate

    one conducting plate is at origin of xy plane. and +q is at distance of d from y-axis in the direction of z axis. then what is induced charge in conducting plate & how charge is distributed on plate?
  38. W

    Total induced charge of an infinite cylindrical conductor

    Homework Statement calculate total induced charge on a charged cylinder. where the surface charge density is given by sigma= 2eEo cos(phi) Homework Equations the total induced charge on the cylinder is Integral of (sigma) da can u calculate this integral fo me ... it very...
  39. 3

    Seperation of the induced charge

    Homework Statement Please look into the attached file. In that you can see a block conductor is moving within the magnetic field which is acting isto the page. What will be the separation of the induced charge? will it be 1 or 2? Homework Equations The Attempt at a Solution By...
  40. J

    Induced charge distribution on two different radius sphere

    Homework Statement Two insulated metal spheres of equal sizes are given equal positive charges. The two spheres are brought very close to each other without touching. Draw the new charge distribution on the spheres if one sphere is much larger than the other. Homework Equations...
  41. E

    How Does Grounding Affect Charge Conservation in Electromagnetic Theory?

    [SOLVED] Griffiths induced charge Homework Statement I am so insanely confused about induced charge. Griffiths does this problem in which a charge q is held a distance d above an infinite grounded conducting plane and then he calculates that the induced charge on the plane is -q (section...
  42. M

    Induced charge - infinite plates

    No numbers here - purely conceptual. Two thin plates carry total surface charge densities of \sigma and \sigma_{1} respectively. An uncharged conducting slab is placed in between the charged plates, and then above \sigma. What are the induced charged densities on the surfaces of the...
  43. M

    Induced charge between/above infinite charged plates

    No numbers here - purely conceptual. Two thin plates carry total surface charge densities of \sigma and \sigma_{1} respectively. An uncharged conducting slab is placed in between the charged plates, and then outside \sigma. What are the induced charged densities on the surfaces of the...
  44. R

    Induced charge in coil from other static coils?

    Hello ALL, I have a question about magnetism and generating electricity in a coil from a group of another coils that are alternately switched on/off (cascade). Would a current be generated from a group of coils that are switched on and off in sequence, having another coil parallel to them...
  45. E

    Induced charge on a grounded conductor

    say there is an infinite grounded conducting plane and a point charge of charge q is above it. the induced charge on the plane is -q and i know how to find this using the method of images to find the potential and then finding and integrating the charge density, but my text says that it should...
  46. quasar987

    Induced charge density by non-uniform dipole density in dielectric?

    In chapter 10 section 3 volume 2 of the Feynman lectures on physics, there is a passage that I can't force myself to agree with. He says, talking about the polarization vector of dielectrics, Can someone explain this perhaps differently? I really don't see how a non-uniform polarisation...