CBSE 2025 · Region 6 · Set 1 · Q24 · 3 marks
State Lenz's law. A rod MN of length L is rotated about an axis passing through its end M perpendicular to its length, with a constant angular velocity $\displaystyle \omega$ in a uniform magnetic field $\displaystyle \overrightarrow{\mathrm{B}}$ parallel to the axis. Obtain an expression for emf induced between its ends.Define 'self-inductance' of a coil. Derive an expression for self-inductance of a long solenoid of cross-sectional area A and length $\displaystyle l$, having n turns per unit length.
State Lenz's law. A rod MN of length L is rotated about an axis passing through its end M perpendicular to its length, with a constant angular velocity $\displaystyle \omega$ in a uniform magnetic field $\displaystyle \overrightarrow{\mathrm{B}}$ parallel to the axis. Obtain an expression for emf induced between its ends.
Define 'self-inductance' of a coil. Derive an expression for self-inductance of a long solenoid of cross-sectional area A and length $\displaystyle l$, having n turns per unit length.
Marking-scheme solution
Lenz's law
The polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it.
Expression of induced emf
The magnitude of the emf generated across the length dr of the rod as it moves at right angles to the magnetic field is given by
\[d\varepsilon = B\mathrm{v}\,dr \]
\[\varepsilon = \int d\varepsilon \]
\[= \int_0^L B\mathrm{v}\,dr \]
\[\varepsilon = \int_0^L B\omega r\,dr \]
\[\varepsilon = \frac{1}{2} B L^2 \omega \]
Alternatively:
Area of the sector (QMN) $\displaystyle = \dfrac{1}{2} L^2 \theta$
Induced emf is $\displaystyle \varepsilon = B \times \dfrac{d}{dt}\left( \dfrac{1}{2} L^2 \theta \right)$
\[\varepsilon = \frac{1}{2} B L^2 \frac{d\theta}{dt} \]
\[\varepsilon = \frac{1}{2} B L^2 \omega \]
Self inductance of a coil is the ratio of the flux linkage to the current flowing in the coil.
Alternatively:
Self inductance of a coil is defined as the flux linked with the coil when unit current flows through it.
Alternatively:
Self inductance of a coil may be defined as the magnitude of emf induced in the coil when current changes at the rate of $\displaystyle 1$ A/s in the coil.
Expression for self inductance of a long solenoid:
The magnetic field due to current flowing in the solenoid, $\displaystyle B = \mu_0 n I$
Total flux linked with the given solenoid
\[N\phi_B = (nl)(\mu_0 n I)\,A \]
\[N\phi_B = \mu_0 n^2 A\, l I \]
Self inductance
\[L = \frac{N\phi_B}{I} \]
\[L = \mu_0 n^2 A\, l \]
Electromagnetic InductionMotional Electromotive ForceApplyshort_answermedium
More from Electromagnetic Induction
- Assertion: The mutual inductance between two coils is maximum when the coils are wound on each other. Reason…2024 · asked 3×
- In the process of charging of a capacitor, the current produced between the plates of the capacitor is:2023 · asked 3×
- A vertically held bar magnet is dropped along the axis of a copper ring having a cut as shown in the diagram.…2025 · asked 3×
- The direction of induced current in the loop abc is:2023 · asked 3×
- (i) Define self-inductance of a coil. Derive the expression for the energy required to build up a current I…2025 · asked 3×
- Two coils C 1 and C 2 are placed close to each other. The magnetic flux φ 2 linked with the coil C 2 varies…2023 · asked 3×
- Assertion: Induced emf produced in a coil will be more when the magnetic flux linked with the coil is more.…2026 · asked 3×
- (i) State Lenz's law and explain how this law is a consequence of conservation of energy principle. (ii) A…2025 · asked 3×
CBSE Class 12 Physics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.