Magnetic Effects of Current and Magnetism - Important Formulas Table

Magnetic Effects of Current and Magnetism - 50 Important Formulas Table

S.No.	Concept / Quantity	Formula	Key Notes
1	Biot-Savart Law	$d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2}$	Basic law
2	Magnetic Field due to Straight Current Carrying Wire	$B = \frac{\mu_0 I}{2\pi r}$	Long straight wire
3	Magnetic Field at Centre of Single Circular Loop	$B = \frac{\mu_0 I}{2R}$	At centre
4	Magnetic Field at Centre of Coil with N turns	$B = \frac{\mu_0 N I}{2R}$	-
5	Magnetic Field on Axis of Circular Loop	$B = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}$	x = distance from centre
6	Magnetic Field inside Long Solenoid	$B = \mu_0 n I$	n = turns per metre
7	Magnetic Field inside Toroid	$B = \frac{\mu_0 N I}{2\pi r}$	r = mean radius
8	Ampere’s Circuital Law	$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{encl}}$	-
9	Lorentz Force on Moving Charge	$\vec{F} = q(\vec{v} \times \vec{B})$	$F = qvB\sin\theta$
10	Force on Current Carrying Conductor	$\vec{F} = I(\vec{l} \times \vec{B})$	$F = IlB\sin\theta$
11	Magnetic Moment of Current Loop	$\vec{m} = I\vec{A}$ (Single turn)	$m = NIA$
12	Torque on Current Loop	$\vec{\tau} = \vec{m} \times \vec{B}$	$\tau = mB\sin\theta$
13	Potential Energy of Magnetic Dipole	$U = -\vec{m} \cdot \vec{B}$	$U = -mB\cos\theta$
14	Magnetic Field due to Bar Magnet (Axial position)	$B = \frac{\mu_0}{4\pi} \frac{2M}{d^3}$	d >> l
15	Magnetic Field due to Bar Magnet (Equatorial position)	$B = \frac{\mu_0}{4\pi} \frac{M}{d^3}$	Opposite to M
16	Relation B, H and Magnetisation	$\vec{B} = \mu_0(\vec{H} + \vec{M})$	-
17	Magnetic Susceptibility	$\chi_m = \frac{M}{H}$	-
18	Relative Permeability	$\mu_r = 1 + \chi_m$	$\mu = \mu_0 \mu_r$
19	Current Sensitivity of Galvanometer	$I_s = \frac{NAB}{k}$	k = torsional constant
20	Voltage Sensitivity of Galvanometer	$V_s = \frac{NAB}{kR}$	-
21	Shunt Resistance (Ammeter)	$S = \frac{G}{n-1}$	n = range factor
22	Series Resistance (Voltmeter)	$R = (n-1)G$	-
23	Magnetic Field due to Finite Straight Wire	$B = \frac{\mu_0 I}{4\pi d} (\sin\theta_1 + \sin\theta_2)$	-
24	Force between Two Parallel Currents	$F = \frac{\mu_0 I_1 I_2}{2\pi d} l$	Attractive/Repulsive
25	Magnetic Dipole Moment of Revolving Electron	$M = \frac{e}{2m} L$ (Orbital)	Bohr Magneton
26	Bohr Magneton	$\mu_B = \frac{e h}{4\pi m_e} = 9.27 \times 10^{-24}$ Am²	-
27	Curie's Law (Paramagnetic)	$M = \frac{C B}{T}$	C = Curie constant
28	Curie-Weiss Law	$\chi_m = \frac{C}{T - T_c}$	For ferromagnetic
29	Hysteresis Loss	$\text{Loss} \propto \text{Area of B-H curve}$	Per cycle
30	Magnetic Flux	$\phi = \vec{B} \cdot \vec{A}$	Weber
31	Magnetic Permeability	$\mu = \mu_0 \mu_r$	-
32	Intensity of Magnetisation	$I = \frac{M}{V}$	-
33	Pole Strength	$m = \frac{M}{2l}$	-
34	Magnetic Field due to Short Bar Magnet (General)	$B = \frac{\mu_0}{4\pi} \frac{M}{d^3} \sqrt{1 + 3\cos^2\theta}$	-
35	Time Period of Vibration Magnetometer	$T = 2\pi \sqrt{\frac{I}{m B_H}}$	-
36	Deflection Magnetometer (Tan A position)	$B = B_H \tan\theta$	-
37	Deflection Magnetometer (Tan B position)	$B = \frac{B_H}{\tan\theta}$	-
38	Cyclotron Frequency	$f = \frac{qB}{2\pi m}$	-
39	Cyclotron Radius	$r = \frac{mv}{qB}$	-
40	Hall Voltage	$V_H = \frac{IB}{n e t}$	-
41	Hall Coefficient	$R_H = \frac{1}{n e}$	-
42	Magnetic Field inside Hollow Solenoid	$B = 0$	Ideal case
43	Self-Inductance of Solenoid	$L = \mu_0 n^2 A l$	-
44	Mutual Inductance (Two Coils)	$M = \frac{\mu_0 N_1 N_2 A}{l}$	-
45	Energy Stored in Magnetic Field	$U = \frac{1}{2} L I^2$	-
46	Energy Density in Magnetic Field	$u = \frac{B^2}{2\mu_0}$	-
47	Magnetic Flux Linkage	$N\phi = LI$	-
48	Force on Charge in Combined E & B Field	$\vec{F} = q\vec{E} + q(\vec{v} \times \vec{B})$	-
49	Velocity Selector	$v = \frac{E}{B}$	-
50	Magnetic Moment of Electron (Spin)	$\mu_s = \frac{e h}{4\pi m_e}$ (Bohr magneton)	g = 2

Important Constants

• $\mu_0 = 4\pi \times 10^{-7}$ T m A⁻¹
• Bohr Magneton $\mu_B = 9.27 \times 10^{-24}$ J/T

Note: This table covers nearly all important formulas required for Class 12 Board Exams, JEE Main, JEE Advanced, and NEET.