Del Operator - Definition & Significance - Coordinate System.


- The collection of partial derivative operators is called DEL operator. Hence DEL can be viewed as the derivative in multi dimensional space.

- DEL operator is defined as a vector differential operator.

- A DEL operator is not a vector in itself, but when acts on a scalar function, it becomes a vector.


- Del is not simply a vector; it is a vector operator. Whereas a vector is an quantity with both a magnitude and direction, DEL does not have a precise value for either until it is allowed to operate on something.

- In Cartesian coordinate system Del operator is given as:



This operator is useful or significant in defining


DEL OPERATOR - CYLINDRICAL CO-ORDINATE SYSTEM:

Unit vectors of Cartesian co-ordinate system are related to unit vectors of Cylindrical co-ordinate system as:

ax = aρ cosφ – aφ sinφ

ay = aρ sinφ + aφ cosφ

az =az

The differential part of x, y in terms of ρ and φ is given as:


Since the del operator is given as:


Substituting the values, we get







DEL OPERATOR - SPHERICAL CO-ORDINATE SYSTEM:

Unit vectors of Spherical co-ordinate system are related to unit vectors of Cartesian co-ordinate system as:

ax = sinθ cosφ ar + cosθ cosφ aθ – sinφ aφ

ay = sinθ sinφ ar + cosθ sinφ aθ + cosφ aφ

az = cosθ ar - sinθ aθ

The differential part of x, y, z in terms of r, θ and φ as:


Substituting the values, we get







ALSO READ:

- Line , Surface and Volume Intergral.

- Del Operator - Definition and Significance.

- Gradient Of a Scalar (∇ V).

- Numericals / Solved Examples - Gradient Of a Scalar.

- Divergence Of a Vector ( ∇ . A ).

- Numericals / Solved Examples - Divergence Of a Vector.

- Curl Of a Vector ( ∇ x A).

- Laplacian Of a Scalar ( ∇2 V).


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