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Q.

Two straight infinitely long current carrying wires lying along the xaxis and yaxis carry currents 100A and 200A as indicated in the adjoining figure. A rigid square metallic wire frame ABCD of side 10cm and resistance (R=10Ω)  is connected to a capacitor C=1mF  as shown in the figure. The wire frame which lies in the xy  plane, moves with a constant velocity 30(i^+j^)m/s. At the instant, when the point A is located at (20cm,20cm) the charge q0  on the capacitor (as shown in the figure) is 0.2μC.  If at the above mentioned instant, the current flowing in the circuit is given by 10n amp. Fill the value of n in nearest integer

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answer is 5.

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Detailed Solution

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The emf induced in the anticlockwise direction in the loop is 

μ01002π.2×0.1×0.1×30μ01002π×3×0.1×0.1×30

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=μ02π×100×30(1213)=104V

The net emf is anticlockwise and is given by  
Apply Kirchoff law along the loop.
+qc+iR=104 i=[104qc]1R=105A.

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Two straight infinitely long current carrying wires lying along the x−axis and y−axis carry currents 100A and 200A as indicated in the adjoining figure. A rigid square metallic wire frame ABCD of side 10cm and resistance (R=10Ω)  is connected to a capacitor C=1mF  as shown in the figure. The wire frame which lies in the x−y  plane, moves with a constant velocity 30(i^+j^)m/s. At the instant, when the point A is located at (20cm,20cm) the charge q0  on the capacitor (as shown in the figure) is 0.2μC.  If at the above mentioned instant, the current flowing in the circuit is given by 10−n amp. Fill the value of n in nearest integer