# What do you mean by solenoidal?

## What do you mean by solenoidal?

Solenoidal has its origin in the Greek word for solenoid, which is σωληνοειδές (sōlēnoeidēs) meaning pipe-shaped, from σωλην (sōlēn) or pipe. In the present context of solenoidal it means constrained as if in a pipe, so with a fixed volume.

## How do you know if a vector field is solenoidal?

If there is no gain or loss of fluid anywhere then div F = 0. Such a vector field is said to be solenoidal.

**What is irrotational and solenoidal field?**

An irrotational vector field is a vector field where curl is equal to zero everywhere. Similarly, an incompressible vector field (also known as a solenoidal vector field) is one in which divergence is equal to zero everywhere.

### What makes a field solenoidal?

Solenoidal fields are characterized by their so-called vector potential, that is, a vector field A such that a=curlA. Examples of solenoidal fields are field of velocities of an incompressible liquid and the magnetic field within an infinite solenoid.

### What is meant by Solinoid?

: a coil of wire usually in cylindrical form that when carrying a current acts like a magnet so that a movable core is drawn into the coil when a current flows and that is used especially as a switch or control for a mechanical device (such as a valve)

**What is meant by solenoid class 10?**

A solenoid is a coil of wire bound across a corkscrew-shaped piston, usually made of iron. The total magnetic field produced by the solenoid can be defined as the amount of vector force provided by each such turn, and the total magnetic field created by the solenoid is equal to that formed by a circular loop.

#### When a vector field is solenoidal and irrotational?

The irrotational vector field will be conservative or equal to the gradient of a function when the domain is connected without any discontinuities. Solenoid vector field is also known as incompressible vector field in which the value of divergence is equal to zero everywhere.

#### How do you know if a vector field is conservative?

This condition is based on the fact that a vector field F is conservative if and only if F=∇f for some potential function. We can calculate that the curl of a gradient is zero, curl∇f=0, for any twice continuously differentiable f:R3→R. Therefore, if F is conservative, then its curl must be zero, as curlF=curl∇f=0.

**What are irrotational field and solenoidal field give examples?**

## What is an irrotational field give example?

A vector field F in R3 is called irrotational if curlF = 0. This means, in the case of a fluid flow, that the flow is free from rotational motion, i.e, no whirlpool. Fact: If f be a C2 scalar field in R3. Then ∇f is an irrotational vector field, i.e., curl(∇f )=0.

## Why magnetic field is solenoidal?

In physics, the term solenoid refers to a long, thin loop of wire, often wrapped around a metallic core, which produces a magnetic field when an electric current is passed through it. Solenoids are important because they can create controlled magnetic fields and can be used as electromagnets.