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A current `I = 3.36(1 +2t) xx 10^(-2)` A increase at a steady state in a long staight wire. A small circular loop of radius `10^(-3)` m has its plane parallel to the wire and is placed at a distance of 1 m from the wire. The resistance of loop is `8.4 xx 10^(-4) (Omega)`. Find the approximate value of induced current in the loop.A. `5.024 xx 24^(-11)A`B. `3.8 xx 24^(-11)A`C. `2.75 xx 24^(-11)A`D. `1.23 xx 24^(-11)A` |
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Answer» Correct Answer - A As the loop is very small the distance of every point in its plane can be taken to be equal to d=1m `I=3.36(I+2t) xx 10^(-2)` ampere `(dI)/(dt)=2xx3.36 xx 10^(-2)m//sec` Magnitude induction at every point on the loop, `B=(mu_(0)I)/(2 pi d)` Magnitude flux linked with loop at any instant, `phi=BA=(mu_(0)I)/(2 pi d)*pi r^(2)` Induced emf, `e=(dphi)/(dt)=(mu_(0)r^(2))/(2d)((dI)/(dt))` Induced current, `I=(e)/(R)=(mu_(0)r^(2))/(Rxx2d) ((dI)/(dt))` `(4 pi xx 10^(-7)xx(10^(-3))^(2) xx 2 xx 3.36 xx 10^(-2))/(8.4 xx 10^(-4) xx 2 xx1)` `=5.024 xx 10^(-11)amp`. |
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