Calculate the magnetic flux density (T) if the magnetic field strength is 2A/m.

Question

Examoogle · Accepted Answer

Option B: $8\pi 	imes 10^{-7}$

Explanation & Concepts:
The magnetic flux density ($B$) in free space is given by the relation $B = \mu_0 H$, where $\mu_0$ is the permeability of free space ($4\pi 	imes 10^{-7} 	ext{ H/m}$) and $H$ is the magnetic field strength. Substituting $H = 2 	ext{ A/m}$, we get $B = (4\pi 	imes 10^{-7}) 	imes 2 = 8\pi 	imes 10^{-7} 	ext{ T}$. Thus, Option B is the correct answer.

Working Principle: In free space or air, magnetic flux density ($B$) is directly proportional to magnetic field strength ($H$). The constant of proportionality is the magnetic permeability of free space, denoted as $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ H/m}$. Therefore, multiplying the magnetic field strength by $\mu_0$ gives the total flux density produced in that region.

Key Formulas: $B = \mu_0 H$ — Relation between magnetic flux density ($B$) and magnetic field strength ($H$) in free space; $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ H/m}$ — Permeability of free space

Key Points: Magnetic field strength ($H$) is measured in Amperes per meter (A/m) or Ampere-turns per meter (AT/m).; Magnetic flux density ($B$) is measured in Tesla (T) or Wb/m².; In a magnetic medium other than free space, $B = \mu H = \mu_0 \mu_r H$ where $\mu_r$ is the relative permeability of the medium.

Applications: Calculation of magnetic field intensity and flux density in electrical machine core designs.; Determining force on current-carrying conductors in magnetic fields.

Additional Info: Option A ($4\pi 	imes 10^{-7} 	ext{ T}$) corresponds to $H = 1 	ext{ A/m}$.. Option B ($8\pi 	imes 10^{-7} 	ext{ T}$) is correct for $H = 2 	ext{ A/m}$.. Option C ($12\pi 	imes 10^{-7} 	ext{ T}$) corresponds to $H = 3 	ext{ A/m}$.

Answer: B is correct — Using $B = \mu_0 H$ with $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ H/m}$ and $H = 2 	ext{ A/m}$ yields $B = 8\pi 	imes 10^{-7} 	ext{ T}$.

Exam Tip: Remember that $B$ and $H$ are related by permeability, similar to how electric flux density ($D$) and electric field intensity ($E$) are related by permittivity ($D = \epsilon E$).

Examoogle · Answer

Option A: $4\pi 	imes 10^{-7}$

Examoogle · Answer

Option C: $12\pi 	imes 10^{-7}$

Examoogle · Answer

Option D: $12.5\pi 	imes 10^{-7}$

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