Question

Relation between Electric Intensity and electric potential​

Answer 1

Answer:

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Explanation:

First let us consider a uniform field, for which the lines of force are parallel and equidistance from each other. Let A and B be two points in a uniform electric field of intensity E.1Let WAB, be the work done to carry a test charge q0 from A to B. Let the potential at A and B be VA and VB, respectively. We have already seen that WAB/q₀ = VB – VA

The work done to carry the test charge from A to B is WAB = q₀EAB

q₀EAB/q₀ = VB – VA

E = (VB – VA)/AB

Let the potential difference VB – VA = V and AB = l

Then E = V/l

The electric field between the two plates separated by a distance d is uniform. If the potential difference between the plates is V. then E = v/ d2To show that E = – dV/dx

Let us consider a non-uniform electric field. The electric intensity varies from one point to another. Let A and B be two points which are very close to each other so that the electric intensity is almost constant.

Let OB = x, AB = dx and OA = x + dx. The potential at B is V and that at A is V – dV. Consider test charge q0 kept at A where electric intensity is E. The force acting on q0 charge at A is F = q0E. The work done to carry q0 charge from A to B through an infinitesimally small displacement dx is dW = F (-dr)

dW = – q₀ Edx, dW/q₀ = -Edx … (1)3But dW/q₀ is the work done in carrying unit test charge from A to B which is the potential difference between the points A and B.

dW/q₀ = VB – VA = V – (V – dV) = dV

From equation (1) dW/q₀ = – Edx

Hence dV = – Edx

E = – dV/dx

dV/ dx is the rate of change of electrostatic potential with distance and is called the potential dx gradient. Thus the electric intensity at a point in an electric field is the negative potential gradient.

Answer 2

Answer:

The relation is very simple. Electric field intensity is equal to the negative of rate of change of potential with respet to the distance or it can be defined as the negative of the rate of derivative of potential difference, V with respect to r, E = - dV/dr.