What does best describe electric field lines?
- There is no electric field inside a charged conductor. A charged conductor at electrostatic equilibrium will contain charges only on its outer surface and will have no net electric field ...
- Charged surfaces align themselves perpendicularly relative to electric fields. ...
- Curvature on the surface of a conductor allows for increased charge concentration. ...
Can two different equipotential lines cross each other?
No, it is not possible for two different equipotential lines to cross. When you go from one line to the next, the potential difference changes gradually until you reach an arbitrary value of an equipotential line.
Why do electric field lines never cross each other?
Electric Field Lines Never Cross Each Otherhttps://www.tutorialspoint.com/videotutorials/index.htmLecture By: Mr. Pradeep Kshetrapal, Tutorials Point India P...
What happens if electric field lines cross each other?
Properties of Electric Field Lines
- The field lines never intersect each other.
- The field lines are perpendicular to the surface of the charge.
- The magnitude of charge and the number of field lines, both are proportional to each other.
- The start point of the field lines is at the positive charge and end at the negative charge.
Why are the equipotentials always perpendicular to the lines of flux?
Back to your original question: why are the Equipotentials always perpendicular to the Lines of Flux? It's because Potentials are a mathematical concept defined as the set of locations along the lines of flux! If we inflate an imaginary sphere, then the individual points on its surface each trace out a perpendicular vector. So, with Earth and gravity, the lines of force are vertical, sticking out of the ground, while the planes of gravity Potential are horizontal planes parallel to the ground. The Earth is surrounded by a dandilion-puff of gravity lines of force, and also surrounded by an invisible onion made of gravity potentials.
What is the difference between electric field and equipotential field?
If i got this straight, electric field is direction of electromagnetic force effected by electric charge on conducting matter. Equipotential lines on other hand are perpendicular lines proportional to forementioned electric field lines where electromagnetic potential is same on every point. So two digferences are:
How to describe potentials?
There's a second way to describe fields. We can see them as mathematical Potentials, as numbers which increase as we travel along a column of vectors in space. (No, not Potential Energy. Just "Potentials.") Mapping out a pattern of potentials is much like mapping out the field-lines: we move a "test charge" in the field, then move it in the direction of the force at that point. As it moves, it increases or decreases in potential. Potentials are like "distance along the lines of force." But not exactly. They're the integral of the vector field: another math concept which isn't as straightforward as flux lines! Here's a way to visualize it: place many test-charges on a charged sphere, then move them outwards along the lines of flux. When they all increase by one unit of potential, they've all moved outwards to form an imaginary hollow sphere. That's the imaginary "Equipotential," where all our test particles are at the same value of potential. Move them more, and when they gain two units, they form a larger hollow sphere. And of course there are more spheres packed between "1" and "2." So, a charged particle would be surrounded by an infinite number of hollow concentric spheres made of Potentials. It looks like an onion, with the original particle in the center. But the Equipotential layers are imaginary of course, since each "layer" can be split into infinitely many.
What is equipotential surface?
So an equipotential surface is a surface of constant height. Think of a mountain. An “equipotential path” around the mountain would be a path that was always at the same height. You are asking about the electric field. Remember that the electric field is the gradient (~ derivative ~ slope) of the potential. Thus, in our analogy, the field is how steep the mountain is. If this connection between potential and field isn’t so comfortable for you you can also think of field and force. Remember that F → = q E →. The stronger the field the bigger the force. In our analogy, the steeper the mountain, the faster a ball placed on it will accelerate downhill.
What does an electric field line show?
Electric field lines show the direction in which it will force the charges to move ,so an electric field line which is not perpendicular will definitely set up a current/emf in the equipotential surface which is contradicting in itself.
What is a field composed of?
One way is to describe fields as being composed of vectors or "flux lines." The lines of flux are imaginary [1], and they arise because we can place a "test charge" [2] into the field, then detect any force upon that "charge." Because of the field, each type of test-charge will experience a force, and the force can be described as a vector having direction and also
How many ways are there to depict fields mathematically?
There are two common ways of depicting fields mathematically.
What happens if your movement is perpendicular to the electric field?
From this equation it becomes evident that if your movement d s → is perpendicular to the E-field then your change in potential is zero. This means that all movement perpendicular to the electric field will result in an equipotenital surface because no work is done when moving a charge on this surface.
What would happen if the lines weren't perpendicular to the surface?
If the lines weren’t perpendicular to the surface, then a component of the field would be present along the surface. This component would represent a change in potential along the surface, which would mean that the surface wasn’t equipotential.
What are the two components of an equipotential surface?
These field lines could then be resolved into two components, one perpendicular to the surface and one along the surface .
How to find electric flux density?
From the Gauss's principle we know that electric flux density = E ∆S cosA. Here A is an angle making the field lines to the equipotential surface, E = electric field of the surface and ∆S is a small area of the surface. But here the surface is equipotential so the change of the flux density = 0. So E ∆S cosA = 0, so cosA = 0, So A =90°. So the field lines are making an angle to the equipotential surface is always 90° or field lines of a point of an equipotential surface is perpendicular to the equipotential surface.
Why do electrons experce an electric force?
Because if they are not perpendicular then there will be a component of E along the surface of conductor. Due to this component, electrons on the suface experence an electric force given by F = qE. As electrons are free to move on the surface of conductor so an electric current produces on the surface of conductor.
How to visualize electric field lines?
One way of visualizing electric field lines and equipotential lines or surfaces is by referring to their gravitational analogue. Consider the topographical map of a hill. The altitude above mean sea level of any point on the hill is analogous to potential in the electrical case.
How to avoid complex maths?
To avoid complex maths, consider a contour map. The contours indicate a linear connection of points at the same altitude. Clearly then a line of maximum slope will be at right-angles to a contour line.
Why is the electric field always perpendicular?
Meaning, if you get any charge from infinity to any point on this surface, equal amount of work is done. Thus if you find this locus it is always perpendicular because of the fact that electric field lines actually represent the gradient in potential.
Why is the electric field perpendicular to the surface?
Because the surface of a conductor [in Fig 3.2] is necessarily a surface of constant potential, the electric field, which is − ∇ φ, must be perpendicular to the surface at every point on the surface
What would happen if electric field lines were not perfectly normal?
If the electric field lines were not perfectly normal, then there would be some tangential component, which would accelerate the charges in the conductor and rearrange the charge distribution. For there to be a uniform distribution, this tangential component must be zero.
How does an electric field affect the conductor?
That means it has a component along the surface. Now, electric fields exert a force on charges, so now we have a force on the charges in the conductor along the surface of the conductor. This force isn't balanced by anything else, so it will then move the charge around. But that means that our system wasn't yet in equilibrium, since charge was moving around. In equilibrium, the charges must be at rest, and that can only be the case when there is no electric force along the surface, i.e., when it's perpendicular to it.
Why is it normal for an electron to be accelerated?
If the surface has different potential, then the electron will be accelerated, then it will automatically become a non equipotential surface. Thats why it should be normal.
What happens if a field is not static?
If it wouldn't be its tangential component would exert a force on the charges and they would move. The condition would then not be static. After some movement and redistribution of charges (when there would be no force on charges) the condition will again become static thus making the field only normal to the surface.
What is the gradient of a scalar field?
Loosely speaking, the gradient of a scalar field (such as the electrostatic potential) points in the direction of that field's greatest change. Since no change occurs in the field when you go along the surface, the gradient shouldn't have a component in that direction.
