Physics Formula Sheet - Electricity and Magnetism

1. Electrostatics

Coulomb’s Law and Electric Field

• Coulomb’s Law: $F = k\frac{q_1q_2}{r^2} = \frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r^2}$
• Electric field: $\vec{E} = \frac{\vec{F}}{q} = \frac{1}{4\pi\epsilon_0}\frac{q}{r^2}\hat{r}$
• Electric field due to dipole (axial): $E = \frac{1}{4\pi\epsilon_0}\frac{2p}{r^3}$
• Electric field due to dipole (equatorial): $E = \frac{1}{4\pi\epsilon_0}\frac{p}{r^3}$

Electric Potential and Capacitance

• Electric potential: $V = \frac{W}{q} = \frac{1}{4\pi\epsilon_0}\frac{q}{r}$
• Potential difference: $V_{AB} = V_A - V_B = -\int_A^B \vec{E} \cdot d\vec{l}$
• Capacitance: $C = \frac{Q}{V}$
• Parallel plate capacitor: $C = \frac{\epsilon_0 A}{d}$
• Energy stored in capacitor: $U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}QV$

2. Current Electricity

Basic Concepts

• Current: $I = \frac{Q}{t}$
• Ohm’s Law: $V = IR$
• Resistance: $R = \rho\frac{L}{A}$
• Power: $P = IV = I^2R = \frac{V^2}{R}$
• Energy consumed: $E = Pt = VIt = I^2Rt$

Combination of Resistances

• Series: $R_{eq} = R_1 + R_2 + R_3 + …$
• Parallel: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + …$

Kirchhoff’s Laws

• Junction rule: $\sum I_{in} = \sum I_{out}$
• Loop rule: $\sum V = 0$

3. Magnetic Effects of Current

Magnetic Field

• Magnetic field due to straight conductor: $B = \frac{\mu_0 I}{2\pi r}$
• Magnetic field at center of circular coil: $B = \frac{\mu_0 I}{2R}$
• Magnetic field on axis of circular coil: $B = \frac{\mu_0 NI R^2}{2(R^2 + x^2)^{3/2}}$

Force on Moving Charge and Current

• Lorentz force: $\vec{F} = q(\vec{v} \times \vec{B})$
• Force on current-carrying conductor: $\vec{F} = I\vec{L} \times \vec{B}$
• Force between parallel conductors: $F = \frac{\mu_0 I_1 I_2 L}{2\pi d}$

4. Electromagnetic Induction

Faraday’s Laws

• Magnetic flux: $\phi = \vec{B} \cdot \vec{A} = BA\cos\theta$
• Faraday’s law: $\varepsilon = -\frac{d\phi}{dt}$
• Induced EMF in moving conductor: $\varepsilon = Blv\sin\theta$

Self and Mutual Induction

• Self inductance: $\varepsilon = -L\frac{dI}{dt}$
• Energy in inductor: $U = \frac{1}{2}LI^2$
• Mutual inductance: $\varepsilon_2 = -M\frac{dI_1}{dt}$

5. AC Circuits

Alternating Current

• Instantaneous voltage: $V = V_0\sin(\omega t + \phi)$
• Instantaneous current: $I = I_0\sin(\omega t + \phi)$
• RMS values: $V_{rms} = \frac{V_0}{\sqrt{2}}$, $I_{rms} = \frac{I_0}{\sqrt{2}}$

Reactance and Impedance

• Capacitive reactance: $X_C = \frac{1}{\omega C} = \frac{1}{2\pi fC}$
• Inductive reactance: $X_L = \omega L = 2\pi fL$
• Impedance in RLC circuit: $Z = \sqrt{R^2 + (X_L - X_C)^2}$
• Resonant frequency: $f_0 = \frac{1}{2\pi\sqrt{LC}}$

6. Electromagnetic Waves

Wave Properties

• Speed of EM waves: $c = \frac{1}{\sqrt{\mu_0\epsilon_0}} = 3 \times 10^8 m/s$
• Energy density: $u = \frac{1}{2}\epsilon_0 E^2 + \frac{1}{2}\frac{B^2}{\mu_0}$
• Intensity: $I = u \times c = \frac{1}{2}\epsilon_0 c E_0^2$

7. Optics

Reflection and Refraction

• Snell’s law: $n_1\sin\theta_1 = n_2\sin\theta_2$
• Critical angle: $\sin\theta_c = \frac{n_2}{n_1}$ (when $n_1 > n_2$)
• Lens maker’s formula: $\frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$
• Lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

Wave Optics

• Young’s double slit: $y = \frac{n\lambda D}{d}$ (bright fringes)
• Diffraction grating: $d\sin\theta = n\lambda$
• Brewster’s law: $\tan\theta_p = n$

This formula sheet covers essential electricity, magnetism, and optics formulas for JEE and NEET preparation. Use this for quick revision during your study sessions.