# Del operator and gradient

DEL OPERATOR

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

$\nabla$ = 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 ($\nabla$ 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)

• 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.

### 4 Responses to Del operator and gradient

1. mirza says:

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

• amit_physics says:

May I know your city? If outside India, then country? I will try for it.
Meanwhile you can post your queries here.