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Formula Sheets / Physics

Chapter 21

Magnetic Effects of Current

Revise with flashcards Download this chapter (PDF) All Physics formulas (PDF)

Biot–Savart and Ampère's laws Force on charges and currents Torque on a loop and galvanometer

Biot–Savart and Ampère's laws

Biot–Savart
$d B = \frac{μ _{0}}{4 π} \frac{I d l \times r ^}{r ^{2}}$
Straight wire
$B = \frac{μ _{0} I}{4 π d} (sin θ_{1} + sin θ_{2});$ infinite: $\frac{μ _{0} I}{2 π d}$
Circular loop
$B_{centre} = \frac{μ _{0} I}{2 R};$ $B_{axis} = \frac{μ _{0} I R ^{2}}{2 ( R ^{2} + x ^{2} ) ^{3/2}};$ arc $\frac{μ _{0} I θ}{4 π R}$
Ampère
$\oint B \cdot d l = μ_{0} I_{enc};$ solenoid $B = μ_{0} n I;$ toroid $B = \frac{μ _{0} N I}{2 π r}$

Force on charges and currents

Lorentz force
$F = q (E + v \times B)$
Circular path
$= v cos θ T$ $T = \frac{2 π m}{q B},$ pitch $= v cos θ T$
Wire
$F = I l \times B;$ parallel wires $\frac{F}{L} = \frac{μ _{0} I _{1} I _{2}}{2 π d}$
Cyclotron frequency
$f = \frac{q B}{2 π m}$

Torque on a loop and galvanometer

$M = N I A,$ $τ = M \times B,$ $U = - M \cdot B$
Moving coil galvanometer
$N I A B = k ϕ \Rightarrow$ current sensitivity $\frac{ϕ}{I} = \frac{N A B}{k}$

Current Electricity Magnetic Properties of Matter