In mathematics and physics, an equipotential or isopotential refers to a region in space where every point is at the same potential. This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentials. An equipotential of a scalar potential function in n-dimensional space is typically an (n − 1)-dimensional space. The del operator illustrates the relationship between a vector field and its associated scalar potential field. An equipotential region might be referred as being 'of equipotential' or simply be called 'an equipotential'.
An equipotential region of a scalar potential in three-dimensional space is often an equipotential surface (or potential isosurface), but it can also be a three-dimensional mathematical solid in space. The gradient of the scalar potential (and hence also its opposite, as in the case of a vector field with an associated potential field) is everywhere perpendicular to the equipotential surface, and zero inside a three-dimensional equipotential region.
Electrical conductors offer an intuitive example. If a and b are any two points within or at the surface of a given conductor, and given there is no flow of charge being exchanged between the two points, then the potential difference is zero between the two points. Thus, an equipotential would contain both points a and b as they have the same potential. Extending this definition, an isopotential is the locus of all points that are of the same potential.
Gravity is perpendicular to the equipotential surfaces of the gravity potential, and in electrostatics and steady electric currents, the electric field (and hence the current, if any) is perpendicular to the equipotential surfaces of the electric potential (voltage).
In gravity, a hollow sphere has a three-dimensional equipotential region inside, with no gravity from the sphere (see shell theorem). In electrostatics, a conductor is a three-dimensional equipotential region. In the case of a hollow conductor (Faraday cage), the equipotential region includes the space inside.
A ball will not be accelerated left or right by the force of gravity if it is resting on a flat, horizontal surface, because it is an equipotential surface.
For the gravity of Earth, the corresponding geopotential isosurface (the equigeopotential) that best fits mean sea level is called the geoid.
Problem:
A given system has the equipotential surfaces shown below, where Vo = 12.0 V.
(a) What are the magnitude and direction of the electric field?
(b) What is the shortest distance one can move to undergo a change in potential of 5.00 V?
I am not too sure on what equations I...
"For a point charge of +3.50 microC what is the radius of the equipotential surface that is at a potential of 2.40 kV?"
For a point charge, the voltage = kq/r, where k =9*10^9 N*m^2/C^2, q is the charge, and r is the radius. Solving for r, I get r = 13.1 m. But the answer is 12.6m...
just a coupla quick questions:
1) in a parallel plate capacitor, we have field lines and equipotential lines. field lines show direction from the + to the - plate, but equipotential lines have no direction. why is this?
2) what happens to the electric field near the edges of the plates?
3) if...
Hey all,
I'm a bit confused over an experiment in which we mapped Equipotential Surfaces to then use to draw Electric Field lines using electrodes placed into water to act as a dipole. Along with this, we also had to place a circular conductor and insulator (both uncharged) into the water as...
Hello everyone I'm confused on this topic. I read about it in the book and it made sense though. The question is: Figure 24-25 shows three sets of cross sections of equipotential surfaces; all three cover the same size region of space.
Diagram: http://www.webassign.net/hrw/25_29.gif
(a)...
We haven't really covered this in class so I need some help.
Assuming that these contours are those of a point charge at the origin, calculate the value of the charge in C.
I tried using the equation kQ/R but that's wrong, I'm not even sure I'm using it right in fact. Any help? Thanks
Field Lines and Equipotential lines
Why can't 2 field lines cross, and why can't 2 equipotential lines cross?
I understand that equipotential lines are perpendicular to field lines. And I see that it'd be impossible to find an equipotential line if two field lines have crossed, since there...
This is the same equipotential lines thread that you may have read
in the Linear and Abstract Algebra.
I have questions…
1. Why don't birds sitting on power cables atop transmission posts get electrocuted? Why do boys get electrocuted when the thread of the kite they are flying...
Indeed, it's me again... asking some questions...
1. Why don't birds sitting on power cables atop transmission posts get electrocuted? Why do boys get electrocuted when the thread of the kite they are flying accidentally touches a power cable?
2. When you walk across a carpeted floor and...