(i) 3.3 X `"10"^{-11}` weber
(ii) 6 X `"10"^{-11}`weber
(iii) 6.6 X `"10"^{-9}`weber
(iv) 9.1 X `"10"^{-11}`weber
(iv) 9.1 X `"10"^{-11}`weber
Explanation:
A circular loop of radius 0.3cm lies parallel to much bigger circular of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with the bigger loop is 9.1 X `"10"^{-11}`weber .
Let flux linked with smaller loop is Փ1 and with bigger loop is Փ2.
Given,
`"R"_{1}` = 0.003 m
X = 15 cm = 0.15 m
Now, `Փ_{1}`=`"B"_{2}``"A"_{1}`
= `\frac{\mu_{o}}{4\pi}``[\frac{2\pi "R"_{2}^{2}l_{2}}{("R"_{2}^{2}+"x"^{2})^{3/2}}]\pi"R"_{2}^{2}`
M = `\frac{\phi_{1}}{l_{2}}` = `\frac{\mu_{0}}{4\pi}``\frac{2\pi "R"_{2}^{2}\pi "R"_{2}^{2}}{("R"_{2}^{2}+"x"^{2})^{3/2}} `
Now, `Փ_{1}`=`"Ml"_{1}`
= `\frac{\mu_{0}}{4\pi}``\frac{2\pi "R"_{2}^{2}\pi "R"_{2}^{2}}{("R"_{2}^{2}+"x"^{2})^{3/2}} ` .`"l"_{1}`
= 9.1 `\times10^{-11}` weber
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