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Q.In an atom electron is moving with the speed of 6.6×1046.6 \times 10^4 ms−1^{-1} in the orbit of radius 0.7 Å. Find the equivalent current in the orbit.

Uttar Pradesh UpmspUP Board (UPMSP) Intermediate 2022Subjective· 2mImportance★★★★★
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A revolving electron is a current loop: i=e/T=ev/(2πr)≈2.4×10−5i=e/T=ev/(2\pi r)\approx2.4\times10^{-5} A.

The orbiting electron passes any point once per revolution, so the equivalent current is charge per period:

i=eT,T=2πrv  ⇒  i=ev2πr.i=\frac{e}{T},\qquad T=\frac{2\pi r}{v}\;\Rightarrow\; i=\frac{ev}{2\pi r}.

Substituting e=1.6×10−19e=1.6\times10^{-19} C, v=6.6×104v=6.6\times10^{4} m s−1^{-1}, r=0.7×10−10r=0.7\times10^{-10} m: …

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