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A current I = 3.36(1 +2t) xx 10^(-2) A i...

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`

Text Solution

Verified by Experts

The correct Answer is:
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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