A uniform magnetic field is restricted within a region of radius r… | NEET 2016 (Phase 2)

Q29NEET 2016 · PHASE 2Medium

Lenz's Law, Eddy Currents & Induced Electric Field

A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate $\frac{d\vec{B}}{dt}$ . Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure. Then the e.m.f. generated is

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Answer: (d)

Induced emf $= -\frac{d\phi}{dt}$ , and flux counts only the area where $B$ exists.
Loop 1 encloses the whole field region of area $\pi r^2$ (not $\pi R^2$ ): $\phi_1 = B\pi r^2 \Rightarrow \varepsilon_1 = -\frac{dB}{dt}\pi r^2$ .
Loop 2 encloses no field: $\phi_2 = 0 \Rightarrow \varepsilon_2 = 0$ .
So the answer is (d) $-\frac{dB}{dt}\pi r^2$ in loop 1 and zero in loop 2.

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