Moving Charges and Magnetism Lecture Notes

Flashcards defining key concepts, formulas, and laws of magnetic fields produced by electric currents and moving charges.

Oersted's Experiment

An experiment demonstrating that an electric current produces a magnetic field around a conductor, which causes a magnetic needle to deflect depending on the current's magnitude and direction.

Magnetic Field Intensity

A vector quantity representing the strength and direction of a magnetic field at any point in space.

Current Element Direction

The spatial vector direction of a current element $d\vec{l}$, defined to be in the exact same direction as the electric current at that point.

Magnetic Field along Wire Length

The condition where the magnetic field at any observation point located directly along the extended length line of a straight current-carrying wire is always zero ($B = 0$).

Magnetic Field Lines of Straight Conductor

Concentric circles formed in a plane perpendicular to a straight current-carrying wire.

Magnetic Field of Infinitely Long Straight Wire

The magnetic field at distance $d$ from an infinitely long current-carrying wire, expressed as $B = \frac{\mu_0 I}{2\pi d}$, showing that $B \propto \frac{1}{d}$.

Magnetic Field of Semi-Infinitely Long Wire

The field at a point near one end of a semi-infinitely long wire, given by $B = \frac{\mu_0 I}{4\pi d}$.

Magnetic Field on Perpendicular Bisector of Finite Wire

The magnetic field produced by a wire of length $L$ at a point on its perpendicular bisector at distance $a$, given by $B = \frac{\mu_0 I L}{2\pi a \sqrt{4a^2 + L^2}}$.

Magnetic Field at Centre of Arc

The magnetic field produced at the center of a circular arc subtending angle $\alpha$ in radians, given by $B = \frac{\mu_0 I \alpha}{4\pi R}$.

Magnetic Field at Centre of Circular Loop

The magnetic field at the center of a circular coil with $N$ turns and radius $R$, given by $B = \frac{\mu_0 N I}{2R}$.

Magnetic Field at Centre of Semicircular Loop

The magnetic field generated at the center of a semicircular current loop, given by $B = \frac{\mu_0 I}{4R}$.

Magnetic Field at Centre of Quarter Circle Loop

The magnetic field generated at the center of a quarter circle arc carrying current $I$, given by $B = \frac{\mu_0 I}{8R}$.

Magnetic Field on Axis of Circular Loop

The magnetic field at a distance $x$ along the axis of a circular coil with $N$ turns and radius $R$, given by $B = \frac{\mu_0 N I R^2}{2(R^2 + x^2)^{3/2}}$.

Magnetic Field Inside an Infinite Solenoid

The uniform magnetic field inside a long solenoid far from its ends, given by $B = \mu_0 n I$, where $n$ is the number of turns per unit length.

Magnetic Field Near End of Infinite Solenoid

The magnetic field on the axis near one end of an infinitely long solenoid, given by $B = \frac{\mu_0 n I}{2}$.

Magnetic Field of a Moving Single Charge

The magnetic field generated by a charge $q$ moving with velocity $\vec{v}$, given by $\vec{B} = \frac{\mu_0}{4\pi} \frac{q (\vec{v} \times \hat{r})}{r^2}$.

Ampere's Circuital Law

A fundamental law stating that the line integral of magnetic field $\vec{B}$ around any closed path is proportional to the total current enclosed by that path, expressed as $\oint \vec{B} \cdot d\vec{l} = \mu_0 I$.