A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate (d⃗B)/(dt). Loop 1 of radius Rr encloses the region r and loop 2 of radius R is outside the region of the magnetic field, as shown in the figure below. Then the emf generated is

Question

A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate (d⃗B)/(dt). Loop 1 of radius R>r encloses the region r and loop 2 of radius R is outside the region of the magnetic field, as shown in the figure below. Then the emf generated is

Accepted Answer

(4) -(d⃗B)/(dt)π r² in loop 1 and zero in loop 2. Faraday's law counts the flux actually enclosed, not the area of the loop. Loop 1 surrounds the whole field region, so the flux through it is Bπ r² however large R is, and ε₁=-d/(dt)(Bπ r²)=-π r²(dB)/(dt). The part of loop 1's area beyond radius r carries no field and adds nothing. Loop 2 lies entirely outside the region, encloses zero flux at all times, and so has ε₂=0.

A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate (d⃗B)/(dt). Loop 1 of radius R>r encloses the region r and loop 2 of radius R is outside the region of the magnetic field, as shown in the figure below. Then the emf generated is

Step-by-step solution

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