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.