Magnetic Field Strength Formula: Derivation & Solved Examples

Magnetic Field Strength or Magnetic Field Intensity is a part of any magnetic field of a certain material that is created from an external current. This is not an inbuilt characteristic of that particular material. The magnetic Field strength can be represented as Vector H, while the measuring unit of it is ampere per meter. Now, any current-generated magnetic field can be represented as B, whereas magnetization of that particular material is represented as M and magnetic permeability of space is μ₀, therefore, the Magnetic Field Strength Formula will be H = B/μ_m = B/μ₀ – M

Key Terms: Magnetic Field Strength, Magnet, Magnetic Field, Current, Metals, Ampere, Vector, Magnetic Field Lines

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What is Magnetic Field Strength?

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Magnetic Fields are formed due to the movement of electric charges along with the internal magnetic properties of any particle. Whereas, the idea of Magnetic Flux can be explained as the total number of Magnetic Field Lines of a certain area.

Hence, the concept of Magnetic Field Strength can be explained as the ratio between MMF, that is necessary for creating a Flux Density within a particular material per unit of its length.

The Magnetic Field Strength Formula is H = B/μ_m = B/μ₀ – M

Magnetic Field Strength

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Properties of Magnetic Field Strength

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Magnetic Field Strength can be easily explained as a way to present the magnetic field intensity. Here are the important properties of Magnetic Field Strength-

• Magnetic Field Strength can not be classified as an intrinsic characteristic of a material.
• It is expressed as the Vector H.
• Magnetic Field Strength varies from material to material.
• Electric Current plays a vital role in the concept of Magnetic Field Strength.
• Magnetic Field Strength can also be represented by the unit Tesla.

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Magnetic Field Strength Formula and Derivation

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The formula for magnetic field magnitude can be represented as B = μ₀I/ 2πr

Where, 

• B = magnetic field magnitude (Tesla, T)
• μ0 = permeability of free space
• I = magnitude of the electric current ( Amperes, A)
• r = distance (m)

Now, if we take this calculation further, 

The Magnetic Field Strength formula is H = B/μ₀ – M

Where, 

• the magnetic field can be represented as B, 
• Magnetization of that particular material is represented as M 
• Magnetic permeability of space is μ₀

Hence, the relationship for B can be represented as 

B = μ₀ (H+M)

Read More: Electric Field Formula

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Solved Examples Of Magnetic Field Strength

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Here are a few solved examples of Magnetic Field Strength or Magnetic Field Intensity-

Ques. The magnetic susceptibility of silicon is −0.4 × 10⁻⁵. Calculate the flux density and magnetic moment per unit volume when a magnetic field of intensity 5 × 10⁵ A/m is applied. 

Ans. From the question, we get to know that, 

χ = –0.4 × 10⁻⁵

H = 5 × 10⁵ A /m

So, we need to find out the value of B and M.

Hence, B = μ₀(H + M) = μ₀ H(1 + χ)

= 4π × 10⁻⁷ × 5 × 10⁵ [1 – 0.4 × 10^-5] = 4π × 5 × 10⁻² × 0.9996 = 0.62 Wb/m²

 And, M = χH = –0.4 × 10⁻⁵ × 5 × 10⁵ = –2.0 A/m.

Ques. What will be the magnetic field strength inside a solenoid that is 2 m long and has 2000 loops, when it carries a 1600 A current?

Ans. To find the magnetic field strength in the magnet coil, we need to use B = μ₀Ni. Additionally, the number of loops per length unit also needed to be considered.

Now, n = Nι = 20002= 1000m^-1 = 10 cm^-1.

And if we put the mentioned values in this, it will be

B = μ₀Ni = (4π10⁻⁷T.mA)(1000m⁻¹)(1600A)

= 2.01 T.

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Things To Remember

• Magnetic Field Strength can be defined as the part of the magnetic field in a material that arises from an external current.
• It is also called magnetic intensity or magnetic field intensity.
• It is expressed as the Vector H.
• Magnetic Field Strength is not an intrinsic characteristic of a material.
• The Magnetic Field Strength Formula is - H = B/μ_m = B/μ₀ – M

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Previous Year Questions

1. The Magnetic Field B In A Circular Coil Does Not D
2. A Solenoid 1 5 M Long And 0 4 Cm In Diameter Posse
3. Four Very Long Wires Are Arranged As Shown So That
4. A Particle Of Mass And Carrying A Charge Enters Wi
5. A Long Conducting Wire Carrying A Current I Is Ben
6. Two Coils Of Inductances L 1 And L 2 Are Linked Su
7. To Shield An Instrument From External Magnetic Fie
8. The Value Of The Magnetic Field Induction At The C
9. The Value Of Horizontal Component Of Earths Magnet
10. The Truthfulness Or Falsity Of A Statement Is Call
11. The True Value Of Angle Of Dip At A Place Is 60 Th
12. The Si Unit Of Magnetic Permeability Is
13. The Neutral Point In The Magnetic Field Of A Horiz
14. The Mathematical Equation For Magnetic Field Lines
15. The Magnetic Field Of Earth At The Equator Is Appr
16. The Magnetic Field Inside A Toroidal Solenoid Of R
17. The Length Of A Solenoid Is 0.1m And Its Diameter