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MHT-CET Physics · Formula sheet

Electromagnetic Induction formulas

10 formulas, 1 reference table and 12 common traps for MHT-CET Physics Electromagnetic Induction, grouped by subtopic.

Full notes with worked examples

Faraday's Law, Lenz's Law and Induced Charge

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Flux, Faraday's Law and Induced Charge

Faraday's law and induced charge

e=−Ndϕdt,q=N ΔϕRe = -N\frac{d\phi}{dt}, \qquad q = \frac{N\,\Delta\phi}{R}

Lenz's Law: the Induced Current Opposes the Change

SituationInduced effect
Magnet dropped through a closed ring or pipefalls with acceleration less than g
Magnet dropped through a cut ringfalls with g — no current
An e.m.f. is still induced across the cut.
Coil and magnet moving togetherno e.m.f.
Flux into a loop increasingcurrent makes a field out of it
Flux into a loop decreasingcurrent makes a field into it
The induced current opposes the CHANGE in flux, not the flux itself.

Common traps

Thinking a faster change moves more charge

A faster change gives a bigger e.m.f. and current, but for less time. The charge q = NΔφ/R is the same however quickly the flux changes.

Using the whole field for the flux

Only the component of B perpendicular to the coil passes through it. For a square in the x–y plane, B=B0(2i^+3j^+4k^)B = B_0(2\hat{i} + 3\hat{j} + 4\hat{k}) gives 4B₀L², not √29 B₀L².

Opposing the flux instead of its change

When the flux is DECREASING, the induced current tries to keep it — its field points the SAME way as the original. It opposes the change, not the field.

Motional e.m.f., Magnetic Braking and Rotating Rods

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Motional e.m.f. Blv

Motional e.m.f.

e=Blve = Blv

Magnetic Braking: Force, Heat and Terminal Speed

Braking force and terminal speed

F=B2l2vR,vt=mgRB2l2F = \frac{B^2l^2v}{R}, \qquad v_t = \frac{mgR}{B^2l^2}

Rotating Rods, Discs, Wheels and Coils

Rotating rod or disc

e=12Bωl2e = \tfrac{1}{2}B\omega l^2

Common traps

Using the total field instead of the cutting component

Only the part of B perpendicular to both the rod and its velocity induces an e.m.f. A rod moving along the field lines induces nothing.

Forgetting that the braking force grows with speed

F = B²l²v/R rises as the rod speeds up, which is why a falling rod reaches a terminal speed instead of accelerating at g forever.

Multiplying by the number of spokes

The spokes of a wheel are in parallel between axle and rim, so the e.m.f. is that of one spoke, ½BωR². More spokes carry more current, not more voltage.

Self-Inductance, the Energy an Inductor Stores, and Inductors Together

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What Self-Inductance Is

Self-inductance

Nϕ=LI,e=−LdIdtN\phi = LI, \qquad e = -L\frac{dI}{dt}

Self-Inductance of a Solenoid

Solenoid

L=μ0μrN2Al=μ0μrn2AlL = \frac{\mu_0 \mu_r N^2 A}{l} = \mu_0\mu_r n^2 A l

Energy in an Inductor, and Inductors in Series and Parallel

Stored energy

U=12LI2U = \tfrac{1}{2}LI^2

Common traps

Forgetting the N in Nφ = LI

The flux 'per turn' must be multiplied by the number of turns. 1500 × 2.8 × 10⁻²/35 is 1.2 H; leaving out N gives 0.8 mH.

Holding N fixed when the question holds n fixed

'Turns per unit length stays the same' means n is fixed, so L = μ₀n²Al grows with BOTH A and l. With N fixed, L = μ₀N²A/l falls as l grows.

Halving the energy when the current halves

Energy goes as I². Half the current stores a quarter of the energy, not half.

Mutual Inductance, Coupling, Transformers and Generators

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Mutual inductance

e2=MdI1dt,Mrings=μ0πr222r1e_2 = M\frac{dI_1}{dt}, \qquad M_{\text{rings}} = \frac{\mu_0\pi r_2^2}{2r_1}

Coefficient of Coupling

Coupling

K=ML1L2K = \frac{M}{\sqrt{L_1L_2}}

Transformers and Generators

Transformer

VsVp=NsNp=IpIs (ideal)\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s}\ \text{(ideal)}

Common traps

Putting the big ring's radius on top

The field comes from the LARGE ring (∝ 1/r₁) and passes through the SMALL ring's area (∝ r₂²): M ∝ r₂²/r₁. The options swap these.

Adding the inductances

Perfectly coupled 25 mH and 9 mH give M = √(25 × 9) = 15 mH, a geometric mean — not 34 or 16.

Scaling current the same way as voltage

A step-up transformer raises the voltage and LOWERS the current: power in ≈ power out. More secondary turns means less secondary current.

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