A solenoid is a coil wound right into a tightly packed helix. In physics, the term solenoid refers to a lengthy, thin loop of wire, frequently wrapped around a metallic core, which produces a magnetic area as soon as an electrical present is passed with it. Solenoids are vital because they can develop controlled magnetic areas and also have the right to be used as electromagnets. The term solenoid refers specifically to a magnet designed to produce a unidevelop magnetic area in a volume of area (wright here some experiment could be brought out).

In engineering, the term solenoid might also describe a variety of transducer tools that convert power right into linear activity. The term is also frequently provided to describe a solenoid valve, which is an included device containing an electromechanical solenoid which actjonathanlewisforcongress.comtes either a pneumatic or hydraulic valve, or a solenoid switch, which is a specific type of relay that internally uses an electromechanical solenoid to operate an electric switch; for example, an auto starter solenoid, or a direct solenoid, which is an electromechanical solenoid.

 You are watching: A solenoid is producing a magnetic field 1 Magnetic area of a solenoid

## Magnetic area of a solenoid

### Inside

This is a derivation of the magnetic field roughly a solenoid that is long enough so that fringe effects have the right to be ignored. In the diagram to the ideal, we instantly recognize that the area points in the positive z direction inside the solenoid, and also in the negative z direction exterior the solenoid.

We watch this by using the ideal hand grip ascendancy for the field about a wire. If we wrap our ideal hand also roughly a wire through the thumb pointing in the direction of the present, the curl of the fingers shows how the area behaves. Since we are dealing with a long solenoid, every one of the components of the magnetic field not pointing upwards cancel out by symmeattempt. Outside, a similar cancellation occurs, and the area is only pointing downwards.

Now consider imaginary the loop c that is located inside the solenoid. By Ampère"s legislation, we know that the line integral of B (the magnetic field vector) around this loop is zero, since it encloses no electrical curleas (it deserve to be additionally assumed that the circuital electrical field passing through the loop is consistent under such conditions: a continuous or constantly altering current with the solenoid). We have actjonathanlewisforcongress.comlly shown above that the field is pointing upwards inside the solenoid, so the horizontal sections of loop c does not contribute anything to the integral. Thus the integral of the up side 1 is eqjonathanlewisforcongress.coml to the integral of the down side 2. Because we deserve to arbitrarily adjust the dimensions of the loop and also get the exact same result, the just physical explanation is that the integrands are actjonathanlewisforcongress.comlly eqjonathanlewisforcongress.coml, that is, the magnetic field inside the solenoid is radially unicreate. Note, though, that nothing prohibits it from differing longitudinally which in truth it does.

### Outside

A comparable argument can be used to the loop a to conclude that the area outside the solenoid is radially unicreate or consistent. This last result, which holds strictly true only near the centre of the solenoid wbelow the area lines are parallel to its size, is important inasa lot as it mirrors that the field exterior is practically zero considering that the radii of the field external the solenoid will certainly tend to infinity.

An intuitive discussion can additionally be offered to show that the field external the solenoid is actjonathanlewisforcongress.comlly zero. Magnetic field lines only exist as loops, they cannot diverge from or converge to a allude prefer electrical area lines have the right to (see Gauss"s legislation for magnetism). The magnetic area lines follow the longitudinal path of the solenoid inside, so they have to go in the opposite direction external of the solenoid so that the lines have the right to form a loop. However, the volume exterior the solenoid is much better than the volume inside, so the density of magnetic area lines outside is considerably diminished. Now recontact that the field outside is consistent. In order for the complete number of area lines to be conoffered, the area external should go to zero as the solenoid gets much longer.

### Qjonathanlewisforcongress.comntitative description

Now we deserve to consider the imaginary loop b. Take the line integral of B around the loop, through the size of the loop l. The horizontal components vanish, and the area external is nearly zero, so Ampère"s Law provides us:

wbelow μ0 is the magnetic consistent, N the number of transforms, i the current.This eqjonathanlewisforcongress.comtion is for a solenoid via no core. The inclusion of a ferromagnetic core, such as iron, boosts the magnitude of the magnetic field in the solenoid. This is expressed by the formula

wright here μr is the family member permecapability of the product that the core is made of. μ0μr is the permecapacity (μ) of the core product such that: