Note that the potential is greatest bigwins (most positive) near the positive charge and least (most negative) near the negative charge. Depending on whether q is positive or negative, the electric field lines for a single charge q are radial lines that begin or finish at the charge. The electric field at each place is clearly normal to the equipotential surface that passes through that point.

(b) The corresponding electric field lines are found by drawing them perpendicular to the equipotentials. Note that these fields are consistent with two equal negative charges. The field has a non-zero component along the surface if it was not perpendicular to the equipotential surface. Work would be required to shift a unit test charge in the opposite direction as the component of the field.

Both have an inverse-square relationship on distance and differ only in the proportionality constants. The masses in the expression of gravitational law are replaced by charges in Coulomb’s law expression. Thus, like the potential energy of a mass in a gravitational field, the electrostatic potential energy of a charge in an electrostatic field is defined.

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Therefore, the gradient always points normal to equipotential surfaces. A surface with an equipotential potential is one where all points on the surface have the same electric potential. This means that at every point on the equipotential surface, a charge will have the same potential energy. One of the most important cases is that of the familiar parallel conducting plates shown in Figure 7.35. Between the plates, the equipotentials are evenly spaced and parallel. The same field could be maintained by placing conducting plates at the equipotential lines at the potentials shown.

For a point charge, equipotential surfaces are spheres centered on the charge. The equipotential surface concept builds clear links to other JEE topics like Gauss’s law, potential energy of electric dipole, and electrostatic potential and capacitance. Practice visualising and mapping surfaces for all typical configurations. Remember, electric field is always highest where equipotential surfaces are closest together. The surface charge density on a long straight metallic pipe is latex\sigma/latex. These have equipotential lines that are parallel to the plates in the space between and evenly spaced.

View this simulation to observe and modify the equipotential surfaces and electric fields for many standard charge configurations. For a uniform electric field E, say, along the x-axis, the equipotential surfaces are planes perpendicular to the x-axis, that is planes parallel to the y-z plane as shown in the above figure. Yes, equipotential surfaces exist for all electric fields, including non-uniform fields.

Move point charges around on the playing field and then view the electric field, voltages, equipotential lines, and more. One of the most important cases is that of the familiar parallel conducting plates shown in Figure 4. The electric field and equipotential lines between two metal plates.

Katy Perry (real name Katheryn Hudson) was born and raised in Southern California. Obviously, two spheres connected by a thin wire do not constitute a typical conductor with a variable radius of curvature. Nevertheless, this result does at least provide a qualitative idea of how charge density varies over the surface of a conductor.