A current $$I=3.36I+2t$$×$$10-2A$$ increases at a steady state in a long straight 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 $$is8.4$$×$$10-4$$Ω. Find the approximate value of induced current in the loop.

Question

A current $$I=3.36I+2t$$×$$10-2A$$ increases at a steady state in a long straight 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 $$is8.4$$×$$10-4$$Ω. Find the approximate value of induced current in the loop.

Infinity Learn · Accepted Answer

As the loop is very small the distance of every point in its plane can be taken to be equal to d $$=$$ $$1$$ $$mI=3.361+2t$$×$$10-2amperedIdt=2$$×$$3.36$$×$$10-2m/secMagnetic$$ induction at every point on the loop'$$)$$, $$B=$$μ$$0I2$$$$π$$dMagnetic flux linked with loop at any instant,ϕ$$=BA=$$μ$$0I2$$$$π$$d.π$$r2Induced$$ emf, $$e=d$$ϕ$$dt=$$μ$$0r22ddIdtInduced$$ current , $$I=eR=$$μ$$0r2R$$×$$2d(dIdt)=4$$π×$$10-7$$×$$(10-3)2$$×$$2$$×$$3.36$$×$$10-28.4$$×$$10-4$$×$$2$$×$$1=5.024$$×$$10-11amp$$

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