Magnetic field induction at centre of circular coil of radius 5 cm and carrying a current 0.9 A is (in S.I. units) (∈0 =absolute permittivity of air S.I. units, velocity of light = 3×108m/s)

B=μ0i2r ∵C=1μ0ε0,μ0=1c2ε0B=ic2ε0×2r=1×9×10−19×1016ε0×5×10−2×2=1ε01016T

Magnetic field induction at centre of circular coil of radius 5 cm and carrying a current 0.9 A is (in S.I. units) (∈0 =absolute permittivity of air S.I. units, velocity of light = 3×108m/s)

B=μ0i2r ∵C=1μ0ε0,μ0=1c2ε0B=ic2ε0×2r=1×9×10−19×1016ε0×5×10−2×2=1ε01016T

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Magnetic field induction at centre of circular coil of radius 5 cm and carrying a current 0.9 A is (in S.I. units) ( $\in_{0}$ =absolute permittivity of air S.I. units, velocity of light = 3×10⁸m/s)

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$\frac{1}{\in_{0} 10^{16}}$

$\frac{10^{16}}{ϵ_{0}}$

$\frac{\in_{0}}{10^{16}}$

$10^{16} \in_{0}$

answer is A.

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Detailed Solution

$B = \frac{μ_{0} i}{2 r} (∵ C = \frac{1}{\sqrt{μ_{0} ε_{0}}}, μ_{0} = \frac{1}{c^{2} ε_{0}})$
$B = \frac{i}{c^{2} ε_{0} \times 2 r} = \frac{1 \times 9 \times 10^{- 1}}{9 \times 10^{16} ε_{0} \times 5 \times 10^{- 2} \times 2} = \frac{1}{ε_{0} 10^{16}} T$