Why do equipotential lines never cross

Work is needed to movea charge from one equipotential line to another. Equipotential lines are perpendicular to electricfield lines in every case. Equipotential lines at different potentials can never cross either. This is because they are , by definition, a line of constant potential. The equipotential at a given point in space can only havea single value. Note: It is possible for two lines representing thesame potential to cross. Asked by: Lora Anistratenko science physics Why do equipotential lines never cross?

Last Updated: 29th July, This is because they are ,by definition, a line of constant potential. The equipotential at a given point in space can only have asingle value. Note: It is possible for two lines representing the same potential to cross. Moira Amsle Professional. Why are equipotential lines important? Work is needed to move a charge from one equipotential line to another. Equipotential lines are perpendicular to electric field lines in every case.

This implies that a conductor is an equipotential surface instatic situations. There can be no voltage difference across thesurface of a conductor, or charges will flow. Walae Asenov Professional. Do equipotential lines have direction? An equipotential line is a line alongwhich the electric potential is constant.

An equipotential surface is a three-dimensional version of equipotentiallines. Equipotential lines are always perpendicular toelectric field lines. Shamira Baston Professional. What is the main cause for the difference in shape of the equipotential lines? Create your own study plan. Join live cram sessions. Live student success coach. Cornell University. Christina K. Andy C. University of Michigan - Ann Arbor. Liev B. Numerade Educator.

Physics Mechanics Bootcamp Lectures Math Review - Intro In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true.

Algebra - Example 1 In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. Recommended Videos Why must field lines be no…. Why must the electric fiel…. Why does a dipole, which h…. The potential for a point charge is the same anywhere on an imaginary sphere of radius r surrounding the charge. An equipotential sphere is a circle in the two-dimensional view of Figure 1.

Since the electric field lines point radially away from the charge, they are perpendicular to the equipotential lines. Figure 1. An isolated point charge Q with its electric field lines in blue and equipotential lines in green. The potential is the same along each equipotential line, meaning that no work is required to move a charge anywhere along one of those lines.

Work is needed to move a charge from one equipotential line to another. Equipotential lines are perpendicular to electric field lines in every case. It is important to note that equipotential lines are always perpendicular to electric field lines. Thus the work is. Work is zero if force is perpendicular to motion. Force is in the same direction as E, so that motion along an equipotential must be perpendicular to E. More precisely, work is related to the electric field by.

Note that in the above equation, E and F symbolize the magnitudes of the electric field strength and force, respectively. In other words, motion along an equipotential is perpendicular to E. One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor.

This implies that a conductor is an equipotential surface in static situations. There can be no voltage difference across the surface of a conductor, or charges will flow.

One of the uses of this fact is that a conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding. Grounding can be a useful safety tool. For example, grounding the metal case of an electrical appliance ensures that it is at zero volts relative to the earth.

A conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding. Because a conductor is an equipotential, it can replace any equipotential surface. For example, in Figure 1 a charged spherical conductor can replace the point charge, and the electric field and potential surfaces outside of it will be unchanged, confirming the contention that a spherical charge distribution is equivalent to a point charge at its center.

Figure 2 shows the electric field and equipotential lines for two equal and opposite charges. Given the electric field lines, the equipotential lines can be drawn simply by making them perpendicular to the electric field lines. Conversely, given the equipotential lines, as in Figure 3a, the electric field lines can be drawn by making them perpendicular to the equipotentials, as in Figure 3b.