Why is the potential difference higher between any two points on a single E-field line than between two points the same distance apart on different E-field lines

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13-07-2022
Physics

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Why is the potential difference higher between any two points on a single E-field line than between two points the same distance apart on different E-field lines

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okpalawalter8 okpalawalter8 · Answer 1 · 2022-07-15T21:06:34+02:00

While moving over a separate electric field line, however, has a non-zero value. If the test charge is transferred in a direction perpendicular to E, no work is done and the electric potential does not change. A smooth equipotential surface characterizes every such path.

Why is the potential difference higher between any two points on a single E-field line than between two points the same distance apart on different E-field lines?

Generally, The equation of the potential difference is mathematically given as

[tex]V = Ed cos \theta.[/tex]

Where

[tex]\theta=Angle[/tex]

E=electric field

d= the varing distance

When the charge to be tested is transferred via an electric field line. Since =0, the maximum possible velocity (Vmax) is calculated.

In conclusion, Since no work is done when the test charge is shifted in a direction perpendicular to E, the electric potential does not shift in this case. Any such route is a smooth equipotential surface.