CBSE Class 12 Physics 2023: question 28

Hints

Open one hint at a time and try again before the next.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. (a) Field inside a long solenoid near the centre: $B={\mu }_{0}nI$

   ½ mark

2. Flux linked with the coil of N turns (cross-section area $\pi r^2$, since wound tightly): $\Phi =NBA=N\pi r^2{\mu }_{0}nI$

   ½ mark

3. Induced emf: $e=-\frac{d\Phi }{dt}=-{\mu }_0\pi r^{2}nN\frac{dI}{dt}$ ...(i)

   ½ mark

4. With $I=I_0\sin \omega t$, $\frac{dI}{dt}=I_0\omega \cos \omega t$, so $e=-{\mu }_0\pi r^{2}nN{I}_0\omega \cos \omega t$

   ½ mark

5. (b) Comparing (i) with $e=-M\frac{dI}{dt}$:

   ½ mark

6. $M={\mu }_0\pi r^{2}nN$

   ½ mark

Answer: (a) $e=-{\mu }_0\pi r^{2}nN{I}_0\omega \cos \omega t$; (b) $M={\mu }_0\pi r^{2}nN$

Revise the chapter

• Chapter: Electromagnetic Induction (notes, formulas, where marks are lost and every past question)
• Topic: Self and Mutual Inductance