What is the significance of closely spaced equipotential lines in terms of electric field and geometrical relationship between equipotentials and electric field lines?
The smaller the spacing between the equipotential lines, the higher the electric field.
Closely spaced electric field lines indicate a strong electric field and closer the lines, the stronger the electric field. 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.If Equipotential lines are closer to each other at a region, it means the electric field is strong at that region. The important thing is to draw them at equal spacing of V (e.g. draw the equipotential lines for V=2.5 V, 3.0 V, 3.5 V… i.e. constant ΔV of 0.5 V). If we do this, equipotential lines can be quite expressive too: The spacing between equipotential lines conveys the magnitude of the field strength. So, the lines of force that are inwards or outwards will always be tangential to the circular equipotential surface. Hence the equipotential line and the line of force will be perpendicular to each other. When the electric field is stronger, the field lines are closer together, and when the electric field is weaker, the field lines are farther apart. This is because the density of field lines is proportional to the magnitude of the electric field. A stronger electric field will have closely spaced equipotential surfaces, while a weaker field will have more widely spaced surfaces. This is because the electric field's strength is related to the potential difference between adjacent equipotential surfaces. A force is experienced when a unit charge or point charge is placed in the electric field of another charged particle. The direction of this force can be represented by the imaginary lines, which are called electric lines of force. Electric lines of force are also known as electric field lines. 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. Equipotential lines are lines connecting points of the same electric potential. All electric field lines cross all equipotential lines perpendicularly. 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 called grounding. Electric field lines are always perpendicular to equipotential lines. This includes the surface of a conductor. Electric field lines never cross and equipotential lines never cross. Electric field lines start on positive charges and end on negative charges. 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.
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