Magnetic field strength formula

The part of the magnetic field in a material that derives from an external current and is not intrinsic to the material itself is known as magnetic field strength, also known as magnetic intensity or magnetic field intensity. Magnetic field strength is one of two ways in which a magnetic field may be expressed. It is distinct from magnetic flux density. Furthermore, when an electric current flows through a wire, a magnetic field is formed. The magnetic field's direction is defined by the current's direction. The magnetic field can be visualised as a sequence of field lines.

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Magnetic field strength

The ratio of the MMF required to create a certain Flux Density within a given material per unit length of that material is referred to as magnetic field strength. It's also known as the magnetic field intensity through certain experts. The magnetic flux also refers to the total number of magnetic field lines that pass through a certain location. Furthermore, when one moves away from a straight current-carrying wire or a straight line connecting two magnetic poles around which the magnetic field is steady, the magnetic flux density decreases. Let’s discuss the strength of magnetic field equation.

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Magnetic field strength formula (Magnetic field intensity formula)

The magnetic intensity formula is followed by,

\[B=\frac{\mu _{0}I}{2\pi r}\]

Where

B = Magnetic field magnitude (T, tesla)

I = Magnitude of the electric current (A, Amperes)

r = Distance (m)

0=Magnitude of the electric current \[\4\pi \times 10^{-7}\]

Electromagnet strength formula

The electromagnet strength formula is as follows,

\[H=\frac{I\times N}{L}\]

Where,

H = Magnetic field Strength of the in ampere-turns/metre.

N = Number of turns of the coil.

I = Current flowing from the coil in amperes.

L = Length of the coil in metres.

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Solved Examples 

Ex.1. Calculate the current magnetic field strength inside a solenoid that is 6 m long. Furthermore, it carries an 1800 A current?

Solution:

Given,

I = 1800 A

r = 6 m

\[\mu _{0}=4\pi \times 10^{-7}T.\frac{m}{a}\]

By using magnetic strength formula (Magnetic intensity formula), we get,

\[B=\frac{\mu _{0}I}{2\pi r}\]

\[B=\frac{4\pi \times 10^{-7}\times 1800}{2\pi \times 6}\]

\[B=\frac{2 \times 10^{-7}\times 1800}{6}\]

B = 6 10^-5 T

The magnetic field strength is 6 10^-5 T.

Ex.2. The current magnetic field strength is 13 10^-6 T inside a solenoid that is 12 m long. Calculate the current carried in a magnetic field?

Solution:

Given,

B = 13 10^-6 T

r = 12 m

\[\mu _{0}=4\pi \times 10^{-7}T.\frac{m}{a}\]

By using the formula of magnetic field intensity, we get,

\[B=\frac{\mu _{0}I}{2\pi r}\]

\[13\times 10^{-6}=\frac{4\pi \times 10^{-7}\times I}{2\pi \times 12}\]

\[\frac{13 \times 10^{-6}\times 12}{2 \times 10^{-7}}=I\]

I = 780 A

Hence the current carried in a magnetic field is 780 A.

Ex.3. Calculate the current magnetic field strength inside a solenoid that is 16 m long. Furthermore, it carries a 620 A current?

Solution:

Given,

I = 620 A

r = 16 m

\[\mu _{0}=4\pi \times 10^{-7}T.\frac{m}{a}\]

By using the formula of magnetic intensity, we get,

\[B=\frac{\mu _{0}I}{2\pi r}\]

\[B=\frac{4\pi \times 10^{-7}\times 620}{2\pi \times 12}\]

\[B=\frac{4\pi \times 10^{-7}\times 620}{12}\]

B = 1.0334 10^-5 T

The magnetic field strength is 1.0334 10^-5 T.