Where are the electric field strongest based on equipotential lines and why electric field is always perpendicular to equipotential surface?
The largest electric field occurs where the equipotential lines are closest to one another because there is a large potential shift over a short space. It would not meet the criteria of equipotential as a charge would experience a force along the surface and the potential would change if the electric field had any component parallel to the surface. As a result, the equipotential surface and the electric field are always perpendicular.
The electric field is the gradient of the potential. If the equipotential lines are closer together, the potential changes by the same amount over a shorter distance. Consequently, the electric field is stronger in this case. As such, we expect the electric field to be strongest at the point where the lines are close together. The electric field is thus strongest at where the factor − Δ V Δ r is greatest. Electric field lines are perpendicular to the equipotential lines, and point "downhill". A conductor forms an equipotential surface. When lines are close to each other, the electric field is strong. The closeness of the lines is directly related to the strength of the electric field. A test charge placed anywhere will feel a force in the direction of the field line; this force will have strength proportional to the density of the lines. If we talk about the magnitude of the electric field, then it will be strongest in the region where they are highly dense. This means that lines are closer to each other but do not cut each other or overlap each other, and when they are far apart, they are weaker in strength. This is because if the electric field is not perpendicular to the equipotential surface there would have existed some nonzero component along the surface. Hence to move a charge along the direction of the field some amount of work had to be done. Equipotential surfaces have equal potentials everywhere on them. For stronger fields, equipotential surfaces are closer to each other! These equipotential surfaces are always perpendicular to the electric field direction, at every point. Equipotential lines are always perpendicular to electric field lines. The process by which a conductor can be fixed at zero volts by connecting it to the earth with a good conductor is grounding.
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