Study sheet: Moving Charges and Magnetism

📋 Course Outline

1. Magnetic Force and Particle Motion
2. Forces on Current-Carrying Conductors
3. Magnetic Fields from Currents
4. Loops, Solenoids, and Ampere Law
5. Galvanometer and Its Conversions

📖 1. Magnetic Force and Particle Motion

📝 Essential Points

📐 Formula — The magnetic force on a charged particle is $F=qvB\sin\theta$, where θ is the angle between velocity and magnetic field.

📐 Formula — In a uniform magnetic field, magnetic force supplies the centripetal force according to $qvB=\frac{mv^2}{r}$.

📐 Formula — The radius, time period, and frequency of a charged particle moving in a circular path are $r=\frac{mv}{qB}$, $T=\frac{2\pi m}{qB}$, and $f=\frac{qB}{2\pi m}$, respectively.

• When the velocity is perpendicular to the magnetic field, the magnetic force is $F=qvB$ and is perpendicular to both the velocity and the magnetic field.

💡 Memory Hook

Magnetic force ⟂ velocity → circular motion

📖 2. Forces on Current-Carrying Conductors

★ Must-know

📐 Formula — The force on a straight current-carrying conductor in a magnetic field is $F=BIl\sin\theta$.

📐 Formula — The force per unit length between two parallel current-carrying conductors separated by distance d is $\frac{F}{l}=\frac{\mu_0 I_1I_2}{2\pi d}$.

📌 Parallel currents flowing in the same direction attract each other, whereas parallel currents flowing in opposite directions repel each other.

Further detail

📐 Formula — For a conductor perpendicular to the magnetic field, the force is $F=BIl$.

💡 Memory Hook

Same-direction currents attract; opposite-direction currents repel

📖 3. Magnetic Fields from Currents

★ Must-know

📐 Formula — The magnetic field due to a long straight current-carrying conductor is $B=\frac{\mu_0I}{2\pi r}$.

📐 Formula — For a circular coil of N turns, area A, and current I in a magnetic field B, the torque is $\tau=NIAB\sin\theta$.

📐 Formula — The magnetic dipole moment of a coil is $M=NIA$.

Further detail

📐 Formula — Biot–Savart law gives the field contribution $dB=\frac{\mu_0}{4\pi}\frac{I\,dl\sin\theta}{r^2}$ from a current element.

📖 4. Loops, Solenoids, and Ampere Law

★ Must-know

📐 Formula — The magnetic field at the centre of a circular loop with N turns and radius R is $B=\frac{\mu_0NI}{2R}$.

📐 Formula — Ampere’s circuital law states that the line integral of magnetic field around a closed path is $\oint\mathbf{B}\cdot d\mathbf{l}=\mu_0I$.

📐 Formula — For a long solenoid with n turns per unit length, the magnetic field inside is $B=\mu_0nI$, or $B=\frac{\mu_0NI}{l}$ when n=N/l.

Further detail

• For a long solenoid, the field outside is approximately zero, and the number of turns in a length l is nl.

💡 Memory Hook

Loop → solenoid → enclosed current

📖 5. Galvanometer and Its Conversions

★ Must-know

📐 Formula — For a moving-coil galvanometer at equilibrium, magnetic torque equals restoring torque: $NIAB=k\theta$.

📐 Formula — The current sensitivity of a galvanometer is $\frac{\theta}{I}=\frac{NBA}{k}$.

📐 Formula — To convert a galvanometer of resistance G and maximum current I_g into an ammeter of range I, the parallel shunt resistance is $S=\frac{I_gG}{I-I_g}$.

📐 Formula — To convert a galvanometer into a voltmeter of range V, the required series resistance is $R=\frac{V}{I_g}-G$.

Further detail

📌 A low-resistance shunt is connected in parallel with the galvanometer to form an ammeter, whereas a high resistance is connected in series with the galvanometer to form a voltmeter.

💡 Memory Hook

Ammeter: low parallel shunt; voltmeter: high series resistance

📊 Synthesis Tables

Galvanometer Conversions

Instrument	Added resistance	Connection	Relation
Ammeter	Low-resistance shunt S	Parallel	$S=\frac{I_gG}{I-I_g}$
Voltmeter	High resistance R	Series	$R=\frac{V}{I_g}-G$