Physics - Magnetism Question with Solution | TestHub

PhysicsMagnetismBiot-savart's & Ampere's Circuital lawEasy2 minPYQ_2020

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A steady current flow in a long wire. It is bent into a circular loop of one turn and the magnetic field at the centre of the coil is $B$ . If the same wire is bent into a circular loop of $n$ turns, the magnetic field at the centre of the coil is

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Answer:

Solution:

The magnetic field a circular coil (for n number of loops)

$B = \frac{μ_{0} n i}{2 r}$

When, $n_{1} = 1, n_{2} = 2$

$2 π r_{1} = n \times 2 π r_{2}$

$\Rightarrow$ $\frac{r_{1}}{r_{2}} = \frac{n}{1}$

So $\frac{B_{1}}{B_{2}} = \frac{\frac{{μ_{0} n}_{1} i}{2 r_{1}}}{\frac{μ_{0} n_{2} i}{2 r_{2}}}$

$\frac{B}{B_{2}} = \frac{n_{1}}{n_{2}} . \frac{r_{1}}{r_{2}}$

$\frac{B}{B_{2}} = \frac{1}{n} . \frac{1}{n}$

$\Rightarrow$ $B_{2} = n^{2} B$

Subject:PhysicsTopic:MagnetismSubtopic:Biot-savart's & Ampere's Circuital law

⏱ 2mℹ️ Source: PYQ_2020

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