CBSE-XI-Physics
35: Magnetic Field due to a Current
- #1Using the formula
F →=qv →×B → and B=μ0i2πr, show that the SI units of the magnetic field B and the permeability constant µ0 may be written as N mA-1 and NA-2 respectively.Ans : Using the relation `` \stackrel{\to }{F}=q\stackrel{\rightharpoonup }{v}\times \stackrel{\to }{B}``, we get
`` B=\frac{F}{qv}``
`` =\frac{F}{Itv}``
`` ``
`` ``
Units of
Force (F) = N
Current (I) = A
Time (T) = s
Velocity (v) = m/s
`` \Rightarrow B=\,\mathrm{\,N\,}/\,\mathrm{\,A\,}-\,\mathrm{\,m\,}``
Now, using the relation `` B=\frac{{\mu }_{0}i}{2\,\mathrm{\,\pi \,}r}``, we get
`` \Rightarrow {\mu }_{0}=B\frac{2\,\mathrm{\,\pi \,}r}{i}=\frac{\,\mathrm{\,N\,}}{\,\mathrm{\,A\,}-\,\mathrm{\,m\,}}\times \frac{\,\mathrm{\,m\,}}{\,\mathrm{\,A\,}}``
`` \Rightarrow {\mu }_{0}\mathit{=}\,\mathrm{\,N\,}/{\,\mathrm{\,A\,}}^{2}``
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