Vector differential operator `del’ is represented by a symbol . Its another name is `nabla’. For three dimensional case, it is defined as

= id/dx + jd/dy + kd/dz

where I, j, k are unit vectors in the directions of co-ordinate axis X, Y and Z respectively.

Del is operated in three ways viz, gradient, divergence and curl, which we will discuss in next three sections.

GRADIENT OF A SCALAR

The gradient of a continuously differentiable scalar function v is defined as

grad v ( v)= idv/dx + jdv/dy +kdv/dz

where i, j, k are the unit vectors along X, Y and Z-axes respectively,

Hence, the gradient of a scalar at any point in a scalar field is a vector.

Lamellar Vector Field Or Non-curl Field Or Conservative Field

A vector field derived from a scalar field by taking its gradient is called lamellar vector field or non-curl or conservative field. An electrostatic field, E is a lamellar field because it can be expressed as (negative) gradient of scalar potential, V that is,

E = -grad V = – (idv/dx + jdv/dy +kdv/dz)

Note:After reading this article, you can answer the following questions:

Define del operator

What is the significance of del operator

name the three operations of del

What is gradient of scalar

What is the significance of gradient

Define lamellar vector field

Define non-curl field

Write the example of lamellar vector field.

I will discuss the del another two operations that is divergence and curl in the next articles.

Reference: This article is referred from my authored book “concepts of electromagnetic field theory” having ISBN 978-81-272-5245-8. In case of any doubt in this article or any other EMFT or physics related article, kindly post in the comment section.

kindly send a soft copy of u r book. text u present here is excellent.plz sir…..

May I know your city? If outside India, then country? I will try for it.

Meanwhile you can post your queries here.