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Moving Charges and Magnetism formulas

Class 12 physics formula sheet for NEET and JEE: the key equations of NCERT chapter 4, the special cases questions are built on, and diagrams where they help.

44 formulas8 sectionsClass 12 · Chapter 43 of 8 sections free

By Sreeraj P, M.Sc Physics · 10+ years teaching NEET and JEE

Most used formulasOther formulas and cases

1Magnetic (Lorentz) force

$$\vec F=q(\vec v\times\vec B),\qquad F=qvB\sin\theta$$
$$\begin{array}{l}\displaystyle \vec F=q(\vec v\times\vec B)\\[6pt]\displaystyle F=qvB\sin\theta\end{array}$$

Always ⟂ to $\vec v$ → does no work; speed and KE stay constant. Zero for charges at rest or moving along $\vec B$. Tesla $=$ N A−1 m−1; 1 G $=10^{-4}$ T.

$$\vec F=q(\vec E+\vec v\times\vec B)$$

Lorentz force with both fields. For $\vec F$ with $\vec B$ unknown, use $\vec F\perp\vec v$ and $\vec F\perp\vec B$: e.g. $\vec a\cdot\vec B=0$.

2Motion in a uniform magnetic field

$$r=\frac{mv}{qB}=\frac{p}{qB}=\frac{\sqrt{2mK}}{qB}=\frac1B\sqrt{\frac{2mV}{q}}$$

$\vec v\perp\vec B$: uniform circle. Same $K$: $r\propto\sqrt m/q$ (proton = alpha); same $V$: $r\propto\sqrt{m/q}$.

$$T=\frac{2\pi m}{qB},\qquad f=\frac{qB}{2\pi m},\qquad \omega=\frac{qB}{m}$$

Independent of speed and radius. Time in field for a semicircle entering at the boundary: $\pi m/qB$.

$$\text{Helix: }r=\frac{mv\sin\theta}{qB},\quad p=v\cos\theta\cdot\frac{2\pi m}{qB}$$
$$\begin{array}{l}\displaystyle \text{Helix: }r=\frac{mv\sin\theta}{qB}\\[6pt]\displaystyle p=v\cos\theta\cdot\frac{2\pi m}{qB}\end{array}$$

$\vec v$ at angle $\theta$ to $\vec B$; pitch $p$ = distance moved along $\vec B$ per turn. Distance along $\vec B$ in $n$ turns $=np$.

Bpitch pr = mv sinθ / qB
$$\sin\theta=\frac{d}{r}\ \ (d

Crossing a field strip of width $d$: deviation $\theta$. If $d\ge r$ the particle turns back (semicircle).

3Crossed fields and cyclotron

$$v=\frac EB$$

Velocity selector: $qE=qvB$, particle goes straight whatever its charge or mass.

+−××××××××vE ↓ , B into page: v = E/B passes straight
$$f_c=\frac{qB}{2\pi m},\qquad K_{\max}=\frac{q^2B^2R^2}{2m}$$

Cyclotron: oscillator frequency = cyclotron frequency; $R$ = dee radius. Cannot accelerate electrons (relativistic mass change) or neutrons.

5 more sections and 31 formulas in the full chapter

  1. 4Biot–Savart law8 formulas · 2 diagrams
  2. 5Ampère's law, solenoid, toroid6 formulas
  3. 6Force on currents3 formulas
  4. 7Current loop as a magnetic dipole7 formulas
  5. 8Moving coil galvanometer and meters7 formulas

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