The figure shows a square loop L of side 5cm which is connected to a network of resistances.

Question:

The figure shows a square loop $\mathrm{L}$ of side $5 \mathrm{~cm}$ which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of $1 \mathrm{~cm} \mathrm{~s}^{-1}$. At some instant, a part of $\mathrm{L}$ is in a uniform magnetic field of 1 $\mathrm{T}$, perpendicular to the plane of the loop. If the resistance of $\mathrm{L}$ is $1.7 \Omega$, the current in the loop at that instant will be close to :

  1. (1) $60 \mu \mathrm{A}$

  2. (2) $170 \mu \mathrm{A}$

  3. (3) $150 \mu \mathrm{A}$

  4. (4) $115 \mu \mathrm{A}$


Correct Option: , 2

Solution:

(2) Induced emf,

$e=B v \ell=1 \times 10^{-2} \times 0.05=5 \times 10^{-4} \mathrm{~V}$

Equivalent resistance,

$R=\frac{4 \times 2}{4+2}+1.7$

$=\frac{4}{3}+1.7 \simeq 3 \Omega$

Current, $i=\frac{e}{R}=\frac{5 \times 10^{-4}}{3} \simeq 170 \mu \mathrm{A}$

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