## Important Derivations for Class 12 Physics Chapter 4 Moving Charges and Magnetism

**Biot Savarts Law**

With the help of experimental results, Biot and Savart arrived at a mathematical expression that gives

the magnetic field at some point in space in terms of the current that produces the field.

Experimentally, it was found that, magnetic field at point P varies as:

(1) $$\mathrm{dB} \propto \mathrm{id} \ell \sin \theta$$ (2) $$\mathrm{dB} \propto \frac{1}{\mathrm{r}^2}$$ $$ \begin{aligned} & \Rightarrow \mathrm{dB} \propto \frac{\mathrm{id} \ell \sin \theta}{\mathrm{r}^2} \\ & \mathrm{~dB}=\frac{\mu_0}{4 \pi} \frac{\mathrm{i} \ell \sin \theta}{\mathrm{r}^2} \end{aligned} $$ here $$ \mu_0=4 \pi \times 10^{-7} \frac{\mathrm{Tm}}{\mathrm{A}}$$ (permeability of free space)Unit of B: T or Wb/m

^{2}

Scalar Form $$ \mathrm{dB}=\frac{\mu_0}{4 \pi} \frac{\mathrm{id} \ell \sin \theta}{\mathrm{r}^2} $$ Vector Form $$ \mathrm{d} \overrightarrow{\mathrm{B}}=\frac{\mu_0}{4 \pi} \frac{\mathrm{i}(\mathrm{d} \vec{\ell} \times \mathrm{r})}{\mathrm{r}^3} $$

## Why students face difficulty in physics derivations?

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

- 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.
- Mathematical background: Physics often involves complex mathematical calculations, and students who struggle with math may find it challenging to perform the necessary calculations.
- Limited practice: Regular practice is key to developing the skills required for physics derivations, and students who have limited practice opportunities may struggle.
- 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.
- 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.
- 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:

- Practice, practice, practice: Regularly practicing physics derivations helps to build muscle memory and improve recall.
- Visualize the process: Try to visualize the steps involved in a derivation, as well as the physical meanings behind each equation.
- 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.
- Write it down: Writing out a derivation helps to solidify your understanding and makes it easier to remember.
- 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.
- Teach someone else: Teaching someone else the derivation can be a great way to reinforce your understanding and remember it more easily.
- 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.