The magnetic field at the centre of a circula | vedclass

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(C) The magnetic field at the centre of a circular coil is given by $B_{C} = \frac{\mu_{0} I}{2 r}$.The magnetic field at a point on the axis at a dis

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$\left(\frac{2}{\sqrt{5}}\right)^{3} B$

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(C) The magnetic field at the centre of a circular coil is given by $B_{C} = \frac{\mu_{0} I}{2 r}$.The magnetic field at a point on the axis at a distance $x$ from the centre is given by $B_{a} = \frac{\mu_{0} I r^{2}}{2(x^{2} + r^{2})^{3/2}}$.Given $x = \frac{r}{2}$,we substitute this into the formula:$B_{a} = \frac{\mu_{0} I r^{2}}{2((\frac{r}{2})^{2} + r^{2})^{3/2}}$$B_{a} = \frac{\mu_{0} I r^{2}}{2(\frac{r^{2}}{4} + r^{2})^{3/2}} = \frac{\mu_{0} I r^{2}}{2(\frac{5r^{2}}{4})^{3/2}}$$B_{a} = \frac{\mu_{0} I r^{2}}{2 \cdot r^{3} \cdot (\frac{5}{4})^{3/2}} = \frac{\mu_{0} I}{2 r} \cdot (\frac{4}{5})^{3/2}$Since $B = \frac{\mu_{0} I}{2 r}$,we have:$B_{a} = B \cdot (\frac{2}{\sqrt{5}})^{3}$.

The magnetic field at the centre of a circular coil of radius $r$,due to current $I$ flowing through it,is $B$. The magnetic field at a point along the axis at a distance $r/2$ from the centre is

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