Plane figures made of thin wires of resistance R = 50 milli ohm/meter are located in a uniform magnetic field perpendicular to the plane of the figures and which
decrease at the rate dB/dt = 0.1 mT/s. Then currents in the inner and outer boundary are (The inner radius a = 10 cm and outer radius b = 20 cm)

Question

Infinity Learn · Accepted Answer

Current in the inner coil $$i1=$$ε$$R=A1R1dBdtLength$$ of the inner $$coil=2$$$$π$$aSo its resistance $$R1=50$$×$$10$$−$$3$$×$$2$$π(a)∴ $$i1=$$π$$a250$$×$$10$$−$$3$$×$$2$$π(a)×$$0.1$$×$$10$$−$$3=10$$−$$4A$$ According to Lenz's law, direction of il is clockwise.  Induced current in outer coil $$i2=$$ε$$2R2=A2R2dBdt$$⇒ $$i2=$$π$$b250$$×$$10$$−$$3$$×(2$$$$π$$$$b)×$$0.1$$×$$10$$−$$3=2$$×$$10$$−$$4A(CW)$$

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