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A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10A. the magnetic field at point O will be $x \times 10^{- 5} T$ . The value of x is ________.

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Detailed Solution

$\vec{B} = \frac{μ_{0} i}{4 π} θ [\frac{1}{r_{1}} - \frac{1}{r_{2}}] K^{a} = \frac{4 π \times 10^{- 7}}{4 π} (\frac{π}{4}) 10 (\frac{1}{3 \times 10^{- 2}} - \frac{1}{5 \times 10^{- 2}}) \hat{k} \overset{⇀}{B} = \frac{π}{3} \times 10^{- 5} T \approx 1 \times 10^{- 5} T$

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A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10A. the magnetic field at point O will be x×10−5T. The value of x is ________.