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Using the formula → F = q → v × → B and B = μ 0 i 2 π r 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. - Physics

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प्रश्न

Using the formula \[\vec{F} = q \vec{v} \times \vec{B} \text{ and } B = \frac{\mu_0 i}{2\pi r}\]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.

संख्यात्मक

उत्तर

Using the relation \[\vec{F} = q v^\rightharpoonup \times \vec{B}\] , we get

\[B = \frac{F}{qv}\]
\[ = \frac{F}{Itv}\]
Units of
Force (F) = N 
Current (I) = A
Time (T) = s
Velocity (v) = m/s
\[\Rightarrow B = N/A - m\]
Now, using the relation
\[B = \frac{\mu_0 i}{2\pi r}\]\[B = \frac{\mu_0 i}{2\pi r}\], we get
\[\Rightarrow \mu_0 = B\frac{2\pi r}{i} = \frac{N}{A - m} \times \frac{m}{A}\]
\[ \Rightarrow \mu_0 = N/ A^2\]
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Force on a Moving Charge in Uniform Magnetic and Electric Fields
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अध्याय 13: Magnetic Field due to a Current - Exercises [पृष्ठ २४९]

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एचसी वर्मा Concepts of Physics Vol. 2 [English] Class 11 and 12
अध्याय 13 Magnetic Field due to a Current
Exercises | Q 1 | पृष्ठ २४९

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