Physics · Electromagnetic Induction · NEET
EMF is not created at the wire because the wire feels the field. Faraday's law says EMF = rate of change of flux THROUGH the loop's enclosed area (ε = -dΦ/dt). If a changing magnetic field passes through the flat area bounded by the loop, the flux changes and an EMF appears, even though the wire itself is in a field-free region. So the correct question is never 'is the wire in the field?' but 'does the loop enclose changing flux?'
Use only the area that actually has field. The flux through loop 1 is Φ = B × (πr²), because the field exists only inside radius r; the extra ring between r and R has zero field and adds nothing. So EMF = -(dB/dt)πr², NOT -(dB/dt)πR². A very common NEET mistake is plugging in πR².
Loop 2's enclosed area has no magnetic field anywhere inside it (the field lives inside radius r, which is completely outside loop 2). So its flux Φ = 0 at all times, and dΦ/dt = 0, giving EMF = 0. It does not matter that the field is changing somewhere far away; that change is not passing through loop 2's area.
Both statements are true and they do not contradict. A changing B does create a swirling induced electric field E even outside radius r. That E can push charges. But the NET EMF around loop 2 is the closed line integral of E, which by Faraday's law equals -dΦ/dt through loop 2. Since loop 2 encloses zero flux, the induced E-field pushes on one side and pulls back equally on the other, and the total EMF around the closed loop cancels to zero. Local E is non-zero; the loop's net EMF is zero.
Here nothing moves. This is 'static' EMF caused purely by a time-changing B (dB/dt), not motional EMF. There is no rod, no velocity, no Bvl. The only rule you need is ε = -dΦ/dt, with Φ = B × (area that has field, enclosed by the loop).
A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate dB/dt. Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field. Then the e.m.f. generated is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Yes, if the changing field passes through the area the coil encloses. EMF depends on enclosed flux (ε = -dΦ/dt), not on the wire touching the field. If the field is entirely outside the enclosed area, EMF is zero.
Flux counts only the region that actually has field. The field exists inside radius r, so Φ = B(πr²). The area between r and R is field-free and contributes zero flux, no matter how big R is.
Yes. A changing magnetic field produces a circulating induced electric field even outside radius r (E is non-zero there). But for a loop enclosing no flux, the net EMF (closed integral of E) is zero because the contributions cancel around the loop.
Static EMF. Nothing moves; the EMF comes purely from dB/dt (time-changing field). There is no velocity, so ε = Bvl does not apply here — only ε = -dΦ/dt.
NTA repeats this exact loop-1 vs loop-2 idea (2016 PYQ) to test whether you use enclosed flux or the loop's geometric size. Getting πr² vs πR² right, and loop 2 = 0, is a guaranteed one-mark decision.
