Which equipotential line has the greatest potential and relationship between the strength of the electric field and the spacing of equipotential lines?
The equipotential line with the greatest potential is the one closest to the positive charge. This is because the electric potential is defined as the work done per unit charge in moving a charged particle from a reference point to a given point in an electric field. Since the work done against the electric field is directly proportional to the potential difference between the two points, it follows that the potential is highest at the point closest to the positive charge, where the electric field is strongest.
The spacing of equipotential lines is inversely proportional to the strength of the electric field. This means that where the electric field is strongest, the equipotential lines are closest together. This is because the equipotential lines represent points of equal potential, so a stronger electric field will cause the potential to change more rapidly over a given distance, resulting in closer spacing of the equipotential lines.
In general, the relationship between the strength of the electric field and the spacing of equipotential lines can be summarized as follows:
- Where the equipotential lines are close together, the electric field is strong.
- Where the equipotential lines are far apart, the electric field is weak.
This relationship can be used to visualize the strength of the electric field in a given region simply by looking at the spacing of the equipotential lines.
The equipotential lines can be drawn by making them perpendicular to the electric field lines, if those are known. Note that the potential is greatest (most positive) near the positive charge and least (most negative) near the negative charge. If we connect the switch in the neutral wire, when the switch is off, the appliance is connected to the higher potential through the live wire the current flows through the live wire to the appliance. 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. 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. The electric field is the gradient of the electrostatic potential, which means that its magnitude is essentially inversely proportional to the spacing between two adjacent equipotentials. The spacing between electric field lines indicates the strength of the electric field, just as the length of vectors indicates the strength of the electric field. The greater the spacing between field lines, the weaker the electric field. 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. The electric field and the equipotential surface are always mutually perpendicular to each other. Since electric lines of force represent the electric field, it follows that these lines are mutually perpendicular with equipotential surfaces. The denser are the lines of force, the stronger is the electric field.
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