Magnetic Field in a Current-Carrying Solenoid
The magnetic field inside the solenoid is parallel to the axis of the core. Beyond the solenoid, the magnetic field is very weak. The purpose of solenoid is to generate a magnetic field, so studying it is very important to understand how magnetic field are distributed around a current carrying solenoid.
Inside the current carrying solenoid, magnetic field are parallel to axis of a solenoid. That is another way of saying that magnetic field is same at all the points inside a current carrying solenoid, that is uniform inside a solenoid. Beyond the solenoid, at very large distance magnetic field is nearly zero.
Formula of Magnetic Field inside a current carrying solenoid
The magnetic field inside a current-carrying solenoid can be calculated using the formula:
[Tex]B = \mu \cdot n \cdot I[/Tex]
Where:
- B is the magnetic field strength inside the solenoid (in Tesla, T),
- [Tex]\mu[/Tex] is the permeability of the material inside the solenoid (in Henry per meter, H/m),
- n is the number of turns per unit length of the solenoid (unitless), and
- I is the current flowing through the solenoid (in Amperes, A).
The derivation of this formula involves considering the magnetic field created by each individual turn of the solenoid and summing up the contributions from all the turns. However, I’ll provide a simplified explanation here.
Consider a solenoid with N turns per unit length, carrying a current I. Each turn of the solenoid acts like a circular current loop, producing a magnetic field at the center of the loop. The magnetic field at the center of a single turn of radius R carrying a current I is given by Ampère’s law as:
[Tex]B_{\text{loop}} = \frac{\mu_0 \cdot I \cdot R^2}{2 \cdot (R^2 + x^2)^{3/2}}[/Tex]
Where:
- [Tex]\mu_0[/Tex] is the permeability of free space (constant, [Tex]4\pi \times 10^{-7}[/Tex] H/m),
- x is the distance from the center of the loop along its axis.
For a solenoid with N turns per unit length and length L, the total number of turns in the solenoid is [Tex]N \cdot L[/Tex]. By symmetry, the magnetic field at the center of the solenoid due to all the turns will be the sum of the magnetic fields from each turn, which gives:
[Tex]B_{\text{sol}} = N \cdot B_{\text{loop}} = \frac{\mu_0 \cdot N \cdot I \cdot R^2}{2 \cdot (R^2 + x^2)^{3/2}}[/Tex]
For a long solenoid [Tex]( L \gg R )[/Tex], the magnetic field at the center of the solenoid can be approximated as constant along the length of the solenoid and is given by:
[Tex]B = \mu_0 \cdot n \cdot I[/Tex]
Where [Tex]n = N/L [/Tex] is the number of turns per unit length of the solenoid.
Solenoid
A solenoid is an electromagnetic device made out of a coil of wire wound around a cylindrical or elongated core, usually comprised of ferromagnetic material like iron or steel. When an electric current flows through a wire coil, it generates a magnetic field surrounding it, which can exert force on objects in the field or cause mechanical motion. In this article, we will learn in detail about solenoid, its working and application.