ε = -dΦ/dt. Calculate EMF when flux changes from 5Wb to 2Wb in 0.1s.

Faraday's Law — EMF Induced in a Coil

Question

A coil experiences a change in magnetic flux from 5 Wb to 2 Wb in 0.1 seconds. Calculate the EMF induced in the coil.

Solution — Step by Step

The induced EMF is given by:

\varepsilon = -\frac{d\Phi}{dt}

The negative sign is Lenz’s Law — it tells us the direction of induced EMF opposes the change. For magnitude calculations (which is what NCERT and board exams usually ask), we drop the negative sign.

Initial flux $\Phi_i = 5$ Wb, final flux $\Phi_f = 2$ Wb.

\Delta\Phi = \Phi_f - \Phi_i = 2 - 5 = -3 \text{ Wb}

The flux has decreased by 3 Wb. This negative value is physically meaningful — flux dropped, so the induced EMF will try to maintain it (Lenz’s Law). But we work with magnitudes here.

|\varepsilon| = \left|\frac{\Delta\Phi}{\Delta t}\right| = \frac{3}{0.1}

\boxed{\varepsilon = 30 \text{ V}}

Why This Works

Faraday’s Law says EMF is proportional to how fast flux changes — not how much total flux exists. A coil sitting in a strong magnetic field with zero flux change induces zero EMF. This is why a transformer only works on AC, not DC.

The unit check confirms our answer: Wb/s = V (Weber per second equals Volt). This is worth remembering for objective questions — if you see Wb/s in options, that’s volts.

For CBSE Class 12, this is a direct application question. For JEE Main, the same concept appears wrapped in loops moving through non-uniform fields or rotating coils — but the core formula never changes.

Alternative Method

If the problem gives you the magnetic field $B$ , area $A$ , and angle $\theta$ instead of flux directly, use:

\Phi = BA\cos\theta

Then find $\Delta\Phi$ and divide by $\Delta t$ as before. For this problem, flux is given directly, so that step is already done for us. The two-step version (find flux first, then find EMF) is the approach for rotating coil problems in JEE.

When flux decreases, the induced current flows in a direction to oppose the decrease — meaning it tries to maintain the original flux. For direction questions, apply the right-hand rule or Lenz’s Law after finding the magnitude.

Common Mistake

Students often write $\Delta\Phi = 5 - 2 = 3$ Wb (initial minus final) and get the right magnitude by accident, but the setup is wrong. Always do final minus initial: $\Delta\Phi = \Phi_f - \Phi_i$ . In a problem where flux increases, doing it backwards gives you a wrong sign and a wrong direction for the induced EMF — which costs marks in CBSE theory questions and JEE integer types.

The other slip is forgetting units. Flux is in Webers (Wb), time in seconds (s), so EMF comes out in Volts automatically. If you’re getting an answer in the thousands or decimals and it doesn’t feel right, check whether you accidentally used milliseconds or converted wrong.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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