Quick questions on Magnetic force on moving charges and current-carrying conductors (QCE Physics Unit 3)

A charge $q$ moving with velocity $\vec{v}$ through a magnetic field $\vec{B}$ experiences a force:

Point your right hand's fingers in the direction of $\vec{v}$, curl them toward $\vec{B}$; the thumb points in the direction of $\vec{F}$ on a positive charge. For a negative charge (electron), reverse the direction.

A wire of length $L$ carrying current $I$ in a magnetic field $\vec{B}$ experiences a force:

Two long parallel wires carrying currents $I_1$ and $I_2$ separated by distance $d$ exert a force per unit length on each other:

Expect a velocity-selector or mass-spectrometer geometry with diagrams and a question on the radius of curvature, or a current-balance stimulus measuring the force between two parallel conductors. Right-hand-rule direction questions are routine.

A common IA2 design measures the force on a current-carrying conductor between the poles of a permanent magnet as a function of current (or wire length), and extracts the field strength $B$ from the slope. Strong reports linearise $F$ vs $I$ and report $B$ with uncertainty.

State the equation for the force on a charge moving in a magnetic field. [2 marks]

A $5.0 \text{ A}$ current carrying conductor of length $0.30 \text{ m}$ sits perpendicular to a $0.40 \text{ T}$ field. Calculate the force and determine its direction using the right-hand rule for current to north and field to east. [3 marks]

A proton ($m = 1.67 \times 10^{-27} \text{ kg}$, $q = 1.6 \times 10^{-19} \text{ C}$) at $3.0 \times 10^6 \text{ m s}^{-1}$ enters a $0.20 \text{ T}$ field perpendicularly. (a) Calculate the radius of the circular path. (b) Determine the period of motion.