v0id19 said:i'll try to rephrase the question:
a continuous, 2 dimensional shape in which of the following planes (a, b, or c) would have an equal potential throughout its entire surface
Hannisch said:There are three dimensions involved.
Remember, an equipotential surface is perpendicular to the electric field--if you draw (or imagine, whichever you find easier) the electric field and define the x-axis, the y-axis and the z-axis, you can find the plane that would always be perpendicular to the field.
Hannisch said:Yes, it'd be vertical, but remember it has a thickness as well.
A new wording might help: The electric field is along the x-axis. If you have the xy plane, as an example, it would go along the x-axis as well, but with a height or something. If two things go along the same axis, can they ever be perpendicular?
Hannisch said:Yes, because something going along the same axis as another thing will never be perpendicular to each other. Hopefully you see why precisely it's ruled out. Try to use the same logic with the other alternatives and you might come up with the correct answer. But try to really understand what you are doing!
Hannisch said:Three dimensions isn't the easiest thing to imagine and it's not the easiest thing to write either. You are correct in that it's the yz plane.
Try to think of it like this or something:
Use a piece of cardboard or something similar--if you put it on the table on the edge and it's facing you, you have a xy plane. If you lie it down on the table you have a xz plane. If you put it on the edge again but with the thin side facing you, that's a yz plane.
Or sort of just think of the z-axis to come out of the paper or something.
And electric fields always exist in three dimensions. If you have a field around a point charge you only draw the field lines parallel to the paper, but you sort of have to imagine that there are field lines going up from the paper and down through the table as well, because the field isn't only limited to going in the two dimensions you can draw (easily).
Therefore, equipotential surfaces also have to exist in three dimensions, right? :)
Equipotential surfaces are imaginary surfaces in a region of space where all points on the surface have the same potential. In other words, the potential at any point on an equipotential surface is constant.
Equipotential surfaces are always perpendicular to electric field lines. This means that the electric field is always tangent to the equipotential surface at any given point.
Equipotential surfaces are important in understanding the behavior of electric charges in a given region. They help us visualize the electric field and understand how charges move in response to it. Additionally, equipotential surfaces allow us to calculate the potential difference between two points in space.
Equipotential surfaces can be calculated by using the equation V = kQ/r, where V is the potential, k is the Coulomb constant, Q is the charge, and r is the distance from the charge. By plugging in different values for r, we can determine the potential at different points and map out an equipotential surface.
No, equipotential surfaces can take on various shapes depending on the distribution of charges in a given region. In the case of a point charge, the equipotential surfaces are spherical. However, for other charge distributions, the equipotential surfaces can be non-spherical and more complex.