Important Derivations for Class 12 Physics Chapter 6 Electromagnetic Induction

Important Derivations for Class 12 Physics Chapter 6 Electromagnetic Induction

(1) Derivation of Emf induced in a rod moving in a uniform magnetic field.

The magnetic flux linked with the area SPQR is: $$ \phi_R=B A \cos \theta=B l x \cos 0=B l x $$ As the rod PQ is moving towards left with a velocity , x is changing and $$ \vec{v}=-\frac{d x}{d t} . $$ Hence: $$ \begin{aligned} & \text { Induced emf, } \varepsilon=-\frac{d \phi_B}{d t} \\ & =-\frac{d(B l x)}{d t} \\ & =-B l \frac{d x}{d t} \\ & \Rightarrow \varepsilon=B l v \end{aligned} $$ This emf is induced in the rod because of the motion of the rod in the magnetic field. Therefore this emf is called motional emf.

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(2) Derivation of EMF induced in a rotating metallic rod in a uniform magnetic field

Let the rotating metallic rod subtends an angle θ in time t with the centre of the circle.

The area of the sector OPQ is given by, $$ \mathrm{A}=\pi \ell^2 \times \frac{\theta}{2 \pi}=\frac{1}{2} \ell^2 \theta $$ The induced emf is $$\varepsilon=\mathrm{B} \cdot \frac{\mathrm{dA}}{\mathrm{dt}}=\mathrm{B} \cdot \frac{\mathrm{d}\left(\frac{1}{2} \ell^2 \theta\right)}{\mathrm{dt}}=\frac{1}{2} \mathrm{~B} \ell^2 \cdot \frac{\mathrm{d} \theta}{\mathrm{dt}}$$ $$ \varepsilon=\frac{1}{2} \mathrm{~B} \ell^2 \cdot \omega \quad\left(\text { where } \omega=\frac{\mathrm{d} \theta}{\mathrm{dt}}\right) $$

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Why students face difficulty in physics derivations?

There can be several reasons why students face difficulty in physics derivations, including:

1. Lack of foundation: A lack of understanding of the underlying concepts and principles can make it difficult to follow the logical steps in a derivation.
2. Mathematical background: Physics often involves complex mathematical calculations, and students who struggle with math may find it challenging to perform the necessary calculations.
3. Limited practice: Regular practice is key to developing the skills required for physics derivations, and students who have limited practice opportunities may struggle.
4. Poor problem-solving skills: Physics problems often require creative problem-solving skills, and students who struggle with this aspect of physics may find derivations particularly challenging.
5. Limited exposure to different problems: Physics derivations can vary widely in their level of complexity, and students who have limited exposure to different types of problems may struggle when faced with a new challenge.
6. Confusion with notation: Physics often uses a specialized notation, and students who are unfamiliar with this notation may struggle to follow the steps in a derivation.

Remembering physics derivations can be a challenge, but here are some tips that may help:

1. Practice, practice, practice: Regularly practicing physics derivations helps to build muscle memory and improve recall.
2. Visualize the process: Try to visualize the steps involved in a derivation, as well as the physical meanings behind each equation.
3. Make connections: Try to relate each step of the derivation to a concept or formula you already know, which can help to reinforce your understanding.
4. Write it down: Writing out a derivation helps to solidify your understanding and makes it easier to remember.
5. Understand the physical meaning: Try to understand the physical meaning behind each equation, which can help you to remember the derivation in a broader context.
6. Teach someone else: Teaching someone else the derivation can be a great way to reinforce your understanding and remember it more easily.
7. Use mnemonics: Creating mnemonics or acronyms can be a helpful way to remember a series of steps in a derivation.

Remember, it takes time and consistent effort to remember physics derivations. Keep practicing and seeking help when needed, and you will likely see improvement over time.

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