CUET UG Physics Electromagnetic Induction Faradays Laws Lenzs Law Motional EMF

Must‑Know (15–20 detailed bullets)

• Faraday’s First Law: Whenever the magnetic flux linked with a circuit changes, an emf is induced in it. Example: Moving a bar magnet towards a coil induces current.
• Faraday’s Second Law: The magnitude of induced emf is equal to the rate of change of magnetic flux through the circuit. Formula: ( \varepsilon = -\frac{d\Phi_B}{dt} ), where ( \Phi_B = \vec{B} \cdot \vec{A} ).
• Magnetic flux ( \Phi_B = BA\cos\theta ); unit is weber (Wb); 1 Wb = 1 T·m².
• Lenz’s Law: The direction of induced emf opposes the change in magnetic flux that produced it. It ensures conservation of energy.
• In a coil of N turns, total induced emf is ( \varepsilon = -N \frac{d\Phi_B}{dt} ).
• Motional emf across a straight conductor moving perpendicular to uniform B: ( \varepsilon = Blv ), where l = length, v = velocity.
• For motional emf, the force on free electrons due to magnetic field causes charge separation, creating electric field until equilibrium.
• A rod of length 1 m moving at 2 m/s perpendicular to 0.5 T field induces emf: ( \varepsilon = 0.5 \times 1 \times 2 = 1\,V ).
• Eddy currents are induced currents in bulk conductors due to changing magnetic fields; they oppose motion (used in electromagnetic damping).
• Self-inductance (L) of a coil: ( \varepsilon = -L \frac{di}{dt} ); SI unit is henry (H); 1 H = 1 V·s/A.
• Mutual inductance (M): ( \varepsilon_2 = -M \frac{di_1}{dt} ); depends on geometry and orientation of two coils.
• Energy stored in an inductor: ( U = \frac{1}{2}LI^2 ).
• The induced emf in a rotating metallic rod about one end in perpendicular B: ( \varepsilon = \frac{1}{2}Bl^2\omega ).
• In a closed loop, if flux increases into the page, induced current is counterclockwise (Lenz’s Law application).
• For a rectangular loop entering a magnetic field region, emf is induced only when flux changes (i.e., during entry/exit).
• Fleming’s Right Hand Rule gives direction of induced current: Thumb → motion, Forefinger → field, Middle finger → current.
• A coil rotating in a magnetic field produces alternating emf — principle of AC generator.
• The negative sign in Faraday’s law (( \varepsilon = -\frac{d\Phi_B}{dt} )) represents Lenz’s Law.
• Eddy currents cause energy loss in transformers; minimized by laminating core.
• verify from NCERT: Exact value of self-inductance for solenoid (formula ( L = \mu_0 n^2 Al )) is derivable from NCERT.

Difficulty Level

Intermediate — Requires conceptual clarity on direction of emf and application of formulas in dynamic situations like motional emf, but direct numericals are common and formula-based.

Common CUET Traps

• Trap: Assuming induced emf depends on magnetic flux rather than rate of change of flux.
  Avoid: Emf is induced only when flux is changing, not when it's high or constant.

• Trap: Using ( Blv ) for motional emf even when velocity is not perpendicular to B.
  Avoid: Use ( \varepsilon = Blv\sin\theta ), where θ is angle between ( \vec{v} ) and ( \vec{B} ); max emf at θ = 90°.

• Trap: Taking induced current direction from Faraday’s law without applying Lenz’s law.
  Avoid: Always determine change in flux first, then apply Lenz’s law to find opposing current direction.

Practice MCQs

Q1. A 0.5 m long conductor moves perpendicular to a uniform magnetic field of 0.4 T with a speed of 3 m/s. What is the induced emf?
A. 0.6 V
B. 1.2 V
C. 0.2 V
D. 0.4 V
Answer: A
Explanation: ( \varepsilon = Blv = 0.4 \times 0.5 \times 3 = 0.6\,V )
Why others fail: B uses length as 1 m (misread), common calculation error.

Q2. According to Lenz’s law, the induced current in a coil will flow such that it:
A. Increases the magnetic flux
B. Opposes the source voltage
C. Opposes the change in magnetic flux
D. Supports the motion of magnet
Answer: C
Explanation: Lenz’s law states induced current opposes the change in flux.
Why others fail: A is opposite; students confuse “opposes change” with “opposes flux”.

Q3. A rectangular loop moves into a uniform magnetic field perpendicular to its plane. The induced emf is:
A. Zero throughout
B. Constant during entry
C. Increases linearly with time
D. Present only during entry and exit
Answer: D
Explanation: Emf is induced only when flux is changing (during entry/exit).
Why others fail: B assumes constant rate means constant emf, but emf is non-zero only during motion across boundary.

Q4. A metallic rod of length l rotates with angular velocity ω about one end in a uniform magnetic field B perpendicular to the plane of rotation. The emf induced between ends is:
A. ( Bl\omega )
B. ( \frac{1}{2}Bl^2\omega )
C. ( Bl^2\omega )
D. ( \frac{1}{2}Bl\omega )
Answer: B
Explanation: Derived from integration of ( d\varepsilon = Bv\,dr ); result is ( \varepsilon = \frac{1}{2}Bl^2\omega ).
Why others fail: A is motional emf for linear motion; students misapply formula.

Q5. Two coils are placed near each other. The mutual inductance M depends on:
A. Current in primary coil
B. Rate of change of current in secondary
C. Number of turns and relative position
D. Material of wire
Answer: C
Explanation: M depends on geometry, number of turns, orientation, and distance — not on current or material.
Why others fail: A is tempting because M relates to flux per unit current, but M itself is independent of current.

Last‑Minute Revision (15–20 one‑liners)

• ⚠️ Induced emf ∝ rate of change of flux, not flux magnitude.
• ⚠️ Lenz’s law ensures conservation of energy — work done against induced current appears as electrical energy.
• ⚠️ Formula: ( \varepsilon = -N \frac{d\Phi}{dt} ) — negative sign is Lenz’s law.
• ⚠️ Motional emf: ( \varepsilon = Blv ) — valid only when B, l, v are mutually perpendicular.
• ⚠️ Direction of induced current: Fleming’s Right Hand Rule (for generators).
• ⚠️ Eddy currents → cause damping and heating; reduced by lamination.
• ⚠️ Self-inductance L: opposes change in current; analogous to inertia in mechanics.
• ⚠️ Unit of inductance: henry (H) = V·s/A.
• ⚠️ Energy stored in inductor: ( \frac{1}{2}LI^2 ).
• ⚠️ Rotating rod emf: ( \varepsilon = \frac{1}{2}Bl^2\omega ).
• ⚠️ AC generator: coil rotation in B → sinusoidal emf via electromagnetic induction.
• ⚠️ No emf induced if conductor moves parallel to magnetic field.
• ⚠️ Magnetic flux ( \Phi = BA\cos\theta ); max when θ = 0° (B ⊥ plane).
• ⚠️ Mutual inductance M: ( \varepsilon_2 = -M \frac{di_1}{dt} ).
• ⚠️ Changing current in one coil induces emf in nearby coil — mutual induction.
• ⚠️ verify from NCERT: Expression for self-inductance of solenoid ( L = \mu_0 n^2 A l ).
• ⚠️ Induced electric field due to changing B is non-conservative — key in Faraday’s law.
• ⚠️ Flux change can occur by changing B, A, or θ — any can induce emf.
• ⚠️ In loop entering B field, current flows only when area in field is changing.
• ⚠️ Mnemonic: “Lenz = Less” — induced current tries to lessen the change.