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(A) The magnetic field induction $B$ at the centre of a circular coil is given by the formula:$B = \frac{\mu_0 I}{2r} \quad \dots(i)$We know the relat

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$\frac{1}{\varepsilon_0 10^{16}}$

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(A) The magnetic field induction $B$ at the centre of a circular coil is given by the formula:$B = \frac{\mu_0 I}{2r} \quad \dots(i)$We know the relationship between the speed of light $c$, permeability $\mu_0$, and permittivity $\varepsilon_0$ as:$c^2 = \frac{1}{\mu_0 \varepsilon_0} \implies \mu_0 = \frac{1}{\varepsilon_0 c^2}$Substituting this into equation $(i)$:$B = \left( \frac{1}{\varepsilon_0 c^2} ight) \frac{I}{2r}$Given values: $I = 0.9 \,A$, $r = 5 \,cm = 5 	imes 10^{-2} \,m$, $c = 3 	imes 10^8 \,ms^{-1}$.$B = \frac{1}{\varepsilon_0 (3 	imes 10^8)^2} 	imes \frac{0.9}{2 	imes 5 	imes 10^{-2}}$$B = \frac{1}{\varepsilon_0 	imes 9 	imes 10^{16}} 	imes \frac{0.9}{10 	imes 10^{-2}}$$B = \frac{1}{\varepsilon_0 	imes 9 	imes 10^{16}} 	imes \frac{0.9}{0.1} = \frac{1}{\varepsilon_0 	imes 9 	imes 10^{16}} 	imes 9$$B = \frac{1}{\varepsilon_0 	imes 10^{16}}$

The magnetic field induction at the centre of a circular coil of radius $5 \,cm$ carrying a current of $0.9 \,A$ is (in $SI$ units) (where $\varepsilon_0$ is the absolute permittivity of air in $SI$ units, and the velocity of light $c = 3 \times 10^8 \,ms^{-1}$):

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