# Del operator and gradient

**DEL OPERATOR**

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.