Relationship Between Electric Field Intensity(E) & Electric Potential(V) - Field Theory.
- The work done per unit charge in moving a test charge from point A to point B is the electrostatic potential difference between the two points(VAB).
VAB = VB - VASimilarly,
VBA = VA – VB
- Hence it’s clear that potential difference is independent of the path taken.
VAB = - VBA
VAB + VBA = 0
- ∫AB (E . dl) + [ - ∫BA (E . dl) ] = 0
- The above equation shows that the line integral of Electric field intensity (E) along a closed path is equal to zero.
- In simple words,
“No work is done in moving a charge along a closed path in an electrostatic field”.
- Applying Stokes’ Theorem to the above Equation, we have:
- If the Curl of any vector field is equal to zero, then such a vector field is called an Irrotational or Conservative Field.
- Hence an electrostatic field is also called a conservative field.
- The above equation is called the second Maxwell’s Equation of Electrostatics.
- Since Electric potential is a scalar quantity, hence dV (as a function of x, y and z variables) can be written as:
- Hence the Electric field intensity (E) is the negative gradient of Electric potential (V).
- The negative sign shows that E is directed from higher to lower values of V i.e. E is opposite to the direction in which V increases.
- An equipotential surface refers to a surface where the potential is constant.
- The intersection of an equipotential surface and a plane results into a path called an equipotential line.
- No work is done in moving a charge from one point to the other along an equipotential line or surface i.e. VA – VB = 0
From the above equation, it’s clear that the electric flux lines and the equipotential surface and normal to each other.
- Because the electric field is the negative gradient of electric potential, the electric field lines are everywhere normal to the equipotential surface and points in the direction of decreasing potential.
- The equipotential lines for a positive point charge. The solid lines show the flux lines or electric lines of force.
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