What is Electrostatic equilibrium: Definition and 29 Discussions

Electrostatic levitation is the process of using an electric field to levitate a charged object and counteract the effects of gravity. It was used, for instance, in Robert Millikan's oil drop experiment and is used to suspend the gyroscopes in Gravity Probe B during launch.
Due to Earnshaw's theorem, no static arrangement of classical electrostatic fields can be used to stably levitate a point charge. There is an equilibrium point where the two fields cancel, but it is an unstable equilibrium. By using feedback techniques it is possible to adjust the charges to achieve a quasi static levitation.

View More On Wikipedia.org
  1. C

    Electrostatic equilibrium problem

    For this problem, I don't understand why this is impossible. Can someone please help? Many thanks!
  2. A

    Unstable or stable electrostatic equilibrium?

    I wonder if you could help me with both I'm stuck, I know that in order to see if the electrostatic equilibrium is stable or not at the center of the ring , the potential energy has to be minimum there. I was going to use Laplace eq. but it allows neither minimum nor maximum. Then I also...
  3. A

    Induction in electrostatic equilibrium conductor

    We know that both the interior and the surface of an electrostatically balanced conductor are equipotential. My question is if when we approach the loaded objects, the surface of the conductor will continue to be an equipotential. If not, then there could be a field line that left the region...
  4. cs44167

    Why Is My Calculation of Electrostatic Equilibrium Incorrect?

    I set the electrostatic force exerted by the object at (0,0) and (3,0) equal to each other, dividing out k and q2. I was left with q1/d^2 for both terms and substituted in the given charges for each object. I then replaced d^2 for the object at (0,0) with “x^2” and d^2 for the object at (3,0)...
  5. Jurtinus

    Coulomb's law, electrostatics?

    Equation: ΣF=Σk(qi)(qj)/(r^2) Question: Considering more than a couple of particles. How can a net force on a charged particle be calculated if Coulomb's law is under the restriction of static forces? Thanks!
  6. A

    There are two charges with charge q and mass m

    There are two charges with charge q and mass m and they are in equilibrium. Then, in the diagram why is my teacher saying that electrostatic force(F)=mg? Below is diagram.
  7. J

    Electric field inside a sphere

    I'm confused with the electric field inside a sphere. The book said that E=keQr/a^3 While one of the properities of electrostatic equilibrium mentioned that the E-field is zero everywhere inside the conductor. Are there any exceptional cases? Thanks in advance.
  8. K

    Are two charges always in electrostatic equilibrium?

    What I studied was that the force on one charge due to another equal charge in the system of two charges was, (say) F; whereas the force on the other charge due to the first charge was found out to be -F. Hence they add up to be zero. So can I say that the two equal charges are in electrostatic...
  9. M

    Electrostatic equilibrium, deflection of a cobweb

    Homework Statement Homework Equations After creating a FBD and analyzing the forces, I get the equation for the angle as ## tan \theta = \frac{k q^2}{m g r^2} ## The Attempt at a Solution [/B] I have tried to find a way to find the distance between the charges ## r ##, but the only way I...
  10. O

    Electrostatic Equilibrium Problem

    Electrostatics Equilibrium Problem-It is required to hold four equal point charges +q each in equilibrium at the corners of a square. Find the point charge that will do this if kept at the center of the square? I am doing the basics of coulomb's law,can anyone explain this to me? I cannot do...
  11. O

    Conductors in Electrostatic Equilibrium

    A long straight metal rod has a radius of 5 cm and a charge per unit length of 30 nC/m. Find the electric field x cm away where distance is perpendicular to the rod.The solution to this uses ## \int E\cdot dA = \dfrac{q_{encl}}{\epsilon_0}##. My question is, why can you use this? I thought...
  12. Y

    Charged conductor in electrostatic equilibrium

    I have read that in electrostatic equilibrium, their are no electric fields or else the charges would be moving. So given a positively charged spherical shell, the positive charges would repel each other and reside on the outside, causing the shell to be in electrostatic equilibrium. But if...
  13. M

    Plate conductor in electrostatic equilibrium

    Homework Statement A thin, square, conducting plate 50.0 cm on a side lies in the xy plane. A total charge of 4.00 x 10-8 C is placed on the plate. Find (a) the charge density on each face of the plate, (b) the electric field just above the plate, and (c) the electric field just below the...
  14. F

    Electrostatic equilibrium (Sphere with cavity)

    Homework Statement Consider a sphere conductor with a inner concentric sphere cavity. The radius of the inside and outside of sphere are 10 cm and 20 cm. The electric field in a point P, along the outer surface has a intensity of 450 N/C and it is directed out of the surface. When a particle...
  15. P

    Electrostatic equilibrium between 3 styrofoam balls

    Homework Statement Three identical small Styrofoam balls (m = 1.95 g) are suspended from a fixed point by three nonconducting threads, each with a length of 52.1 cm and with negligible mass. At equilibrium the three balls form an equilateral triangle with sides of 28.3 cm. What is the common...
  16. R

    ElectroStatic Equilibrium problem

    Homework Statement particle 1 of charge q1 (at origin) and particle 2 of charge q2 = 3q1, are held at separation L on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y...
  17. L

    A question about Volume charge density and electrostatic equilibrium

    The concept of volume charge density is an even distribution of charge over a three dimensional area. C/m^3. However, the concept of electrostatic equilibrium says that all of a conductors charge lies on the surface of the conductor. The existence of one seems, to me at least, to render the...
  18. J

    Question about electrostatic equilibrium?

    Two fixed charges, 3.0 uC and 5.0 uC, are 0.40 m apart. The 3.0 uC is to the left of the 5.0 uC charge. Where should a third charge of 2.0 uC be placed to put the system of three charges in electrostatic equilibrium? The answer should be measured with respect to the 5.0 uC charge. What...
  19. I

    Can a Conductor Maintain Electrostatic Equilibrium Without Free Charges?

    Homework Statement When books of elctromagnetism talk about Electrostatic equilibrium,they say electric charges will keep moving if electric field in the conductor doesn't equal to zero utill it does.However,what if there are no excess free charges in the area where that doesn't equal to...
  20. D

    Conductors in Electrostatic Equilibrium problem

    Homework Statement In fair weather, over flat ground, there is a downward electric field of about 150 N/C. A) assume that the Earth is a conducting sphere with charge on its surface. If the electric field just outside is 150 N/C pointing radially inwards, calculate the total charge on the...
  21. S

    Question about electrostatic equilibrium for a conductor

    At equilibrium, a conducting object will have no electric field, current or excess charge in its interior. There's a fairly simple derivation for how an initial (non-equilibrium) interior charge density d0 falls to zero exponentially with time t when the conductor approaches equilibrium. For a...
  22. T

    Conducting Spheres in Electrostatic Equilibrium

    Homework Statement Homework Equations potential, V = kq/r where k is 1/4 pi epsilon conservation of charge, sum of q = Q The Attempt at a Solution what i did is let q1 + q2 + q3 = 4*10^-4 then let V1 = V2 = V3 and solve for q3 but i end up getting q3 = 0.0002 which is...
  23. H

    Electric field strength before reaching the state of electrostatic equilibrium

    Homework Statement In such a picture, http://i1021.photobucket.com/albums/af335/hectoryx/electrostaticequilibrium_1.jpg Induced charges will emergence on the left and right side of non-perfect conductor B, because the effect of the electric field of conductor A. As is known to all, when...
  24. K

    Help with Conductors in Electrostatic Equilibrium

    Can someone please help me with this problem. I don't even know where to begin after drawing the picture. Two identical conducting spheres each having a radius of 0.500 cm are connected by a light 1.80 m long conducting wire. A charge of 63.0 µC is placed on one of the conductors. Assume the...
  25. S

    Gauss's Law 2 concentric cylinders in electrostatic equilibrium

    Homework Statement Consider the cross sections of two, very long, concentric, metallic, hollow cylinders placed in a vacuum. The small cylinder has inner radius A and outer radius B while the larger cylinder has inner radius 2A and outer radius 2B. Initially the small and big hollow...
  26. A

    What is mean by charge in an electrostatic equilibrium ?

    what is mean by "charge in an electrostatic equilibrium" ?? In my textbook the definition of the potential difference is that "The workdone on a unit positive charge carrying it from one point to the other kepping the charge in electrostatic equilibrium" In my textbook electrostatic mean...
  27. Y

    Experimental proof of electrostatic equilibrium

    Hey, In my physics we derived certain properties of conductors in electrostatic equilibrium using Gauss' law. One property seemed to "mathematical" to me. It says that the whole charge of a conductor in electrostatic equilibrium is located at the surface. The proof is at follows. Since the...
  28. E

    Electrostatic Equilibrium: Where to Place a Third Charge?

    "Two charges, q1, and q2, are located at the origin and at (0.50m, 0), respectively. Where on the x-axis must a third charge, q3, of arbitrary sign be placed to be in electrostatic equilibrium if (a) q1 and q2 are like charges of equal magnitude, (b) q1 and q2 are unlike charges of equal...
  29. K

    Electrostatic equilibrium and Gauss' law

    A conducting spherical shell of ineer radius a and outer radius b carries a net charge Q. A point charge q is placed at the center of this shell. Determine the surface charge densit on (a) the ineer surface of the shell and (b) the outer surface of the shell. I'm not sure of my reasoning...