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Magnetic Field due to a Current — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMagnetic Field due to a Current2 Marks
Question
Using the formula $\overrightarrow{\text{F}}=\text{q}\overrightarrow{\text{v}}\times\overrightarrow{\text{B}}$ and $\text{B}=\frac{\mu_0\text{i}}{2\pi\text{r}},$ show that the SI units of the magnetic field B and the permeability constant $\mu_0$ may be written as N/A-m and $NA^2$ respectively.
✓

Answer

$\overrightarrow{\text{F}}=\text{q}\overrightarrow{\text{v}}\times\overrightarrow{\text{B}}$
$\text{B}=\frac{\text{F}}{\text{qv}}=\frac{\text{F}}{\text{ITv}}=\frac{\text{N}}{\text{A.sec}/\text{sec}.}=\frac{\text{N}}{\text{A-m}}$
$\text{B}=\frac{\mu_0\text{I}}{2\pi\text{r}}$
$\mu_0=\frac{2\pi\text{rB}}{\text{I}}=\frac{\text{m}\times\text{N}}{\text{A-m}\times\text{A}}=\frac{\text{N}}{\text{A}^2}$

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