Physics

Physics

Problem

A proton (mass 1.67×10−27 kg1.67\times10^{-27}\,\text{kg}, charge +e+e) enters a uniform magnetic field of 0.50 T0.50\,\text{T} with speed 3.0×107 m s−13.0\times10^{7}\,\text{m\,s}^{-1} directed at 45∘45^{\circ} to the field. Determine the distance it advances along the field direction while completing 55 full turns.
Intuitive explanation

When a charged particle enters a magnetic field at an angle, its velocity splits into two independent components: one parallel to the field (which the magnetic force ignores) and one perpendicular (which causes circular motion). The key is recognizing that the proton spirals—it circles in the plane perpendicular to the field while drifting steadily along the field direction. To find how far it advances, calculate the period of one complete circle, multiply by 5 turns, then use the parallel velocity component and that time interval.

Intuitive explanation

When a charged particle enters a magnetic field at an angle, its velocity splits into two independent components: one parallel to the field (which the magnetic force ignores) and one perpendicular (which causes circular motion). The key is recognizing that the proton spirals—it circles in the plane perpendicular to the field while drifting steadily along the field direction. To find how far it advances, calculate the period of one complete circle, multiply by 5 turns, then use the parallel velocity component and that time interval.

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