Equipotential lines are curved lines on a map which mark out lines of identicalaltitude. The altitude pertains to electric potential or voltage. They are always perpendicular to the electric field. The lines creates equipotential surfaces in a three dimensions. Movement along an equipotential surface needs no work since such movement is always perpendicular to the electric field. The figure below shows the equipotential surfaces in dashed lines and electric field lines in solid lines produced by a positive point charge. In this case, the equipotential surfaces are spheres are on the center of the charge.
Equipotential Lines in a Constant Field
In a conducting plate like in a capacitor, the electric field lines are perpendicular to the plates and the equipotential lines are parallel to the plates.
The illustration below shows the electric field of a positive point charge.The electric field is fixed away from the charge and potentialis positive at any set distance from the charge. If the charge moves in the direction of the electric field it will move towards the lower values of potential. If the charge moves towards the direction opposite to that of electric field we move towards the higher values of potential.
The illustration below shows the electric field of a point negative charge.
Limited distance is negative at any point from the charge. If the charge moves toward the direction of the electric field and in the direction of decreasing U thus, becoming move negative. If a charge moves in the direction opposite to electric field, the increasing value of V thus, become less negative. Hence, the moving with the direction of electric field means moving in the direction of decreasing V and moving against the direction of electric field means moving in the direction of increasing V. Therefore, potential difference canbe expressed in terms of electric field as:
Electric field (E) as a function of potential can be expressed as
where Er is the component of electric field along the direction of dv/dr is known as the potential gradient and the negative sign infers that electric field acts in a direction of decrease of potential. The expression above indicates that E is not certainly zero if V is zero.
The illustration shows a graph of a set of equipotential surfaces in a cross section. Each is marked according to its electric potential. A +2.3 10-7 C point charge is at point A. Determine the work done on the point charge by the electric force when it is moved about (a) from point A to point B (b) from point A to point C.
Work done on a charge q by the electric field when the charge moves from potential [tex]V_i[/tex] to potential [tex]V_f[/tex] is computed as [tex]Work =-q(V_f-V_i)[/tex] Since [tex]V_i = V_f [/tex], therefore, it will be zero since both points lie on the same equipotential curve.