Moving Charges and Magnetism

Comprehensive practice flashcards covering the principles of moving charges, magnetism, force laws, and instrument calibration based on physics lecture notes.

When and by whom was the relationship between electricity and magnetism first observed?

In the summer of $1820$, Danish physicist Hans Christian Oersted noticed that a current in a straight wire caused a deflection in a nearby magnetic compass needle.

According to Oersted's findings, how do iron filings arrange themselves around a current-carrying wire?

They arrange themselves in concentric circles with the wire as the centre.

In the adopted convention, how are currents or fields depicted when they emerge out of or go into the plane of the paper?

A dot ($\odot$) represents a field emerging out of the plane, while a cross ($\otimes$) represents a field going into the plane.

What is the formula for the Lorentz force acting on a point charge $q$ moving with velocity $\mathbf{v}$ in the presence of an electric field $\mathbf{E}$ and a magnetic field $\mathbf{B}$?

$$\mathbf{F} = q [ \mathbf{E}(\mathbf{r}) + \mathbf{v} \times \mathbf{B}(\mathbf{r}) ]$$

Under what condition does the magnetic force on a moving charge vanish?

The magnetic force vanishes if the velocity and the magnetic field are parallel or anti-parallel.

Is any work done by the magnetic force on a moving charged particle?

No, because the magnetic force is always perpendicular to the velocity of the particle, resulting in no change in the magnitude of the velocity.

How is the SI unit tesla ($T$) defined?

The magnitude of magnetic field $B$ is $1$ SI unit when the force acting on a unit charge ($1\,C$), moving perpendicular to $B$ with a speed $1\,m/s$, is one newton.

What is the relationship between the tesla and the gauss?

$$1\,gauss = 10^{-4}\,tesla$$

What is the magnetic force $F$ exerted on a straight rod of length $l$ carrying a steady current $I$ in an external magnetic field $B$?

$$\mathbf{F} = I\mathbf{l} \times \mathbf{B}$$

What is the radius $r$ of the circular path described by a charged particle of mass $m$ and charge $q$ moving perpendicular to a uniform magnetic field $B$?

$$r = \frac{mv}{qB}$$

What is the expression for the cyclotron frequency (angular frequency $\omega$) of a charged particle in a magnetic field?

$$\omega = \frac{qB}{m}$$

What is defined as the 'pitch' in helical motion of a charged particle?

The distance moved along the magnetic field in one rotation ($p = v_{\parallel}T$).

State the vector notation of the Biot-Savart law for a magnetic field $d\mathbf{B}$ due to an element $d\mathbf{l}$.

$$d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{r}}{r^3}$$

What is the exact value of the permeability of free space $\mu_0$ in SI units?

$$\mu_0 = 4\pi \times 10^{-7}\,Tm/A$$

Write the expression for the magnetic field $B$ at the center of a circular current loop of radius $R$ carrying current $I$.

$$B = \frac{\mu_0 I}{2R}$$

State Ampere’s circuital law in integral form.

$$\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I$$

What is the magnetic field $B$ at a distance $r$ from a long, straight infinite current-carrying wire?

$$B = \frac{\mu_0 I}{2\pi r}$$

What is the magnetic field $B$ inside a long solenoid with $n$ turns per unit length carrying current $I$?

$$B = \mu_0 n I$$

What is the interaction rule for the magnetic force between parallel and anti-parallel currents?

Parallel currents attract each other, and anti-parallel currents repel each other.

How was the ampere defined in $1946$ based on the force between conductors?

The ampere is the steady current which, maintained in two long parallel conductors placed $1\,metre$ apart in vacuum, produces a force of $2 \times 10^{-7}\,newtons$ per metre of length.

What is the magnetic moment $\mathbf{m}$ of a planar current loop?

$\mathbf{m} = I \mathbf{A}$ (or $m = NIA$ for $N$ turns).

What is the torque $\tau$ experienced by a current loop in a uniform magnetic field $\mathbf{B}$?

$$\mathbf{\tau} = \mathbf{m} \times \mathbf{B}$$

How is a moving coil galvanometer converted into an ammeter?

By attaching a small resistance $r_s$, called a shunt resistance, in parallel with the galvanometer coil.

How is a moving coil galvanometer converted into a voltmeter?

By connecting a large resistance $R$ in series with the galvanometer.

Why does doubling the number of turns in a galvanometer double current sensitivity but leave voltage sensitivity unchanged?

Doubling turns ($N$) doubles the resistance ($R$) of the coil as well; since voltage sensitivity is proportional to $\frac{N}{R}$, the increase in turns is cancelled by the increase in resistance.