The magnetic field at the centre of a circula | vedclass

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Question

Magnetic field at centre of current-carrying coil.

$B_{c}=\frac{\mu_{0} I}{2 r}.........(i)$

Magnetic field at axial point due to a currentcarry

Vedclass · Accepted Answer

$2\sqrt 2 :1$

Vedclass · Answer

Magnetic field at centre of current-carrying coil.

$B_{c}=\frac{\mu_{0} I}{2 r}.........(i)$

Magnetic field at axial point due to a currentcarrying coil at distance of $\mathrm{r}$

$\mathrm{d}=\mathrm{r}$

$\mathrm{B}=\frac{\mu_{0} \mathrm{Ir}^{2}}{2\left(\mathrm{r}^{2}+\mathrm{d}^{2}ight)^{3 / 2}} \Rightarrow \mathrm{B}_{\mathrm{a}}=\frac{\mu_{0} \mathrm{Ir}^{2}}{2\left(2 \mathrm{r}^{2}ight)^{3 / 2}}........(ii)$

$\mathrm{Now}$

$\frac{\mathrm{B}_{\mathrm{c}}}{\mathrm{B}_{\mathrm{a}}}=\frac{\mu_{0} \mathrm{I}}{2 \mathrm{r}} 	imes \frac{2\left(2 \mathrm{r}^{2}ight)^{3 / 2}}{\mu_{0} \mathrm{Ir}^{2}}=2 \sqrt{2}$

$B_{c}: B_{a}=2 \sqrt{2}: 1$

The magnetic field at the centre of a circular current carrying-conductor of radius $r$ is $B_c$. The magnetic field on its axis at a distance $r$ from the centre is $B_a$. The value of $B_c$ : $B_a$ will be

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