What is electric potential derive the relation between electric field intensity and electrostatic potential at a point taking electric field due to a point charge q?
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The change of electric potential with respect to distance is called potential gradient. It is denoted by dv/dx.
The value of electric potential (V) as electric field intensity (E) at distance ‘x’ from the charge ‘Q’ is given by
V=14πϵoQx…(i)
V=14πϵoQx…(i)
E=14πϵoQx2…(i)
E=14πϵoQx2…(i)
differentiating equation (i) with respect to 'x' we get,
d(v)dx=ddx(14πϵoQx)
d(v)dx=ddx(14πϵoQx)
=Q4πϵoddx(x−1)
=Q4πϵoddx(x−1)
=Q4πϵo(−1)x−1−1
=Q4πϵo(−1)x−1−1
=−(Q4πϵo1x2)
=−(Q4πϵo1x2)
=−E
=−E
∴E=−dVdx
∴E=−dVdx
hence, the negative of potential gradient is equal with electric field intensity.
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