Question

Definite electric field intensity. Show that the electric feild at any point is equal to the negative of the potential gradiant at that point.

Answer 1

Answer:

The electric field Intensity at a point is the force experienced by a unit positive charge placed at that point. Electric Field Intensity is a vector quantity. ... Formula: Electric Field = F/q.

LET A LINE TO REPRESENTED AS FOLLOWS:-

o---------------------------------------------A----------B----⇒----∞

let a positive test charge at B {q₀} the force acting outwards given as F=qE

let distance between a and b is dr

now work done in moving that test charge from point b to a is given as

angle between force and direction taken vector is 180,

dw=F.dr cos180°

dw=qE.dr{-1}

dw= -qE.dr......................{1}

this work done can also be calculated as ,

POTENTIAL AT A - POTENTIAL AT B = dw/q

{ v+dv}-{v}=dw/q

dv=dw/q

dw=dv.q........................................{2}

equating {1} and {2}....................

dv.q=-qE.dr

E= -dv/dr

i.e electric field is equal to negative of potential gradient....................................{proof}

note:- you may ask why potential at A is {v+dv} and at B as {v},

ELABORATION:-

WE know,

v∝1/r

so from point o,nearer distance is at A, AS r is less that potential is more, so it taken as {v+dv}

and at B AS {v}