Magnetic Field Strength Formula: Derivation & Solved Examples

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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

Table of Content

What is Magnetic Field Strength?
Properties of Magnetic Field Strength
Magnetic Field Strength Formula and Derivation
Solved Examples of Magnetic Field Strength
Things to Remember
Previous Year Questions
Sample Questions

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

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

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.

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

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

Previous Year Questions

Sample Questions

Ques 1. What is Magnetic Field Strength? (3 Marks)

Ans. The idea 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. It is also called Magnetic Field Intensity. It is represented by Vector H.

Ques 2. What are the basic properties of Magnetic Field Intensity? (3 Marks)

Ans. Magnetic Field Intensity is a part of any magnetic field of a certain material that is created from an external current. Here are the important properties of Magnetic Field Intensity-

Magnetic Field Intensity is not an intrinsic characteristic of a material.
It is expressed as the Vector H.
Magnetic Field Strength varies from material to material.
Magnetic Field Strength can also be represented by the unit Tesla.

Ques 3. What will be the magnetic field strength of a 5 m long solenoid of 800 loops carrying a current of 1700 A? (3 Marks)

Ans. We know that,

B = μ₀NI

n = 800/5 = 160 m^-1

B = (4π x 10^-7 T m/A) x (160 m^-1) x (1700 A)

B = 0.314 T

Ques 4. What is the unit of magnetic field strength H? (1 Mark)

Ans. The Magnetic Field Strength H can be calculated by the unit A/m (ampere per meter).

Ques 5. What will be the magnetic field strength of a 12 m long solenoid of 700 loops carrying a current of 600 A? (3 Marks)

Ans. B = μ₀NI

n = 700/12

n = 58.33 m^-1

Next, B = (4π x 10^-7 T m/A) x (58.33 m^-1) x (600 A)

B = 0.04398 T

Ques 6. What affects magnetic field strength? (3 Marks)

Ans. Here are the things that can affect magnetic field strength-

Type of Material.
Amount of Electric Current.
Size of the wire.
And presence of an Iron Core.

Ques 7. What is the SI unit Of Magnetic Field Strength? (1 Mark)

Ans. The SI Unit for Magnetic Field Strength is Tesla.

Ques 8. Where is the magnetic field strongest? (1 Mark)

Ans. The Magnetic Field is strongest at the Poles.

Ques 9. Calculate the Magnetic Field Strength of a 12 m long solenoid of 700 loops carrying a current of 800 A. (3 Marks)

Ans. B = μ₀NI

n = 700/12 = 58.33 m^-1

Next, B = (4π x 10^-7 T m/A) x (58.33 m^-1) x (800 A)

B = 0.05864 T

Ques 10. What is the Magnetic Field Strength Formula? (3 Marks)

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

Where,

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

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Magnetic Field Strength Formula: Derivation & Solved Examples

What is Magnetic Field Strength?

Properties of Magnetic Field Strength

Magnetic Field Strength Formula and Derivation

Solved Examples Of Magnetic Field Strength

Things To Remember

Previous Year Questions

Sample Questions

CBSE CLASS XII Related Questions

1.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

3.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

4.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

5.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

Similar Physics Concepts

Comments

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Magnetic Field Strength Formula: Derivation & Solved Examples

What is Magnetic Field Strength?

Properties of Magnetic Field Strength

Magnetic Field Strength Formula and Derivation

Solved Examples Of Magnetic Field Strength

Things To Remember

Previous Year Questions

Sample Questions

CBSE CLASS XII Related Questions

1.Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

3.Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

4. If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

5.Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

2.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

3.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

4.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

5.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]