A plane loop, shaped as two squares of sides a $$=$$ $$1$$ m and b $$=0.4$$ m is introduced into a uniform magnetic field⊥to the plane of loop (figure). The magnetic field varies as $$B=10-3$$ $$sin$$(100t) T. The amplitude of the current induced in the loop if its resistance per unit length is $$r=5m$$Ωm−$$1$$ is

Question

A plane loop, shaped as two squares of sides a $$=$$ $$1$$ m and b $$=0.4$$ m is introduced into a uniform magnetic field⊥to the plane of loop (figure). The magnetic field varies as $$B=10-3$$ $$sin$$(100t) T. The amplitude of the current induced in the loop if its resistance per unit length is $$r=5m$$Ωm−$$1$$ is

Infinity Learn · Accepted Answer

ϕ (flux$$ $$linked)  $$=a2Bcos$$⁡$$0$$∘−$$b2Bcos$$⁡$$180$$∘ $$=a2$$−$$b2B$$ $$E=$$−dϕ$$dt=$$−$$a2$$−$$b2dBdt$$ $$=a2$$−$$b2B0$$ω$$cos$$⁡ωt where $$B=B0$$,$$sin$$⁡ωt,$$B0=10$$−$$3T$$,ω$$=100$$∴ $$Imax=a2$$−$$b2B0$$ωR and $$R=(4a+4b)r=4(a+b)r$$∴ $$Imax=(a$$−$$b)B0$$ω$$4r=(1$$−$$0.4)$$×$$10$$−$$3$$×$$1004$$×$$5$$×$$10$$−$$3=3A$$

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A plane loop, shaped as two squares of sides a = 1 m and b =0.4 m is introduced into a uniform magnetic field⊥to the plane of loop (figure). The magnetic field varies as B=10-3 sin(100t) T. The amplitude of the current induced in the loop if its resistance per unit length is r=5mΩm−1 is

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