### Long Question Solution # Electrostatics - Long Question Answer 8

Question: Establish relation between electric field intensity and potential gradient.
Ans: Let A and B are two points on a line of force due to a point charge +Q, as shown in the figure. These points are so close that electric field intensity (E) is constant between them. Work done in taking a unit charge from B to A = Force * displacement
= - E dx ….... (i)
(.: E = F/q| for unit charge q| = 1 .: E = F)
Negative sign shows that force on the unit charge and displacement are in opposite directions.
If the potential difference between A and B is dV, (A is at higher potential), then work done in taking a unit charge from B to A = dV …..... (ii)

From (i) and (ii), we get
dV = -E dx
E = dV/dx …….. (iii)
Thus, electric field strength is equal to the negative of the potential gradient. The direction of E is always in the direction of decrease of potential.

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