What path does a charged particle follow if it enters a uniform magnetic field with velocity perpendicular to the field?

State the radius of circular motion for a charged particle moving perpendicular to a uniform magnetic field.

What happens to the speed of a charged particle moving in a magnetic field if no other forces act?

Derive the circular-path radius from magnetic force and centripetal force.

A proton moves at \(2.0\times10^5\,\mathrm{m\,s^{-1}}\) perpendicular to \(0.50\,\mathrm{T}\). Find its circular radius.

An electron moves at \(3.0\times10^6\,\mathrm{m\,s^{-1}}\) perpendicular to \(0.020\,\mathrm{T}\). Find its circular radius.

How does the radius change if the particle speed doubles while \(m\), \(|q|\), and \(B\) stay fixed?

How does the radius change if the magnetic field doubles while \(m\), \(|q|\), and \(v\) stay fixed?

State the angular speed of circular motion for a charged particle in a uniform magnetic field.

State the period of circular motion for a charged particle in a uniform magnetic field.

A particle has velocity with components both perpendicular and parallel to \(\vec B\). What kind of path results?

In helical motion, which speed component determines the radius?

What happens to the curvature direction if the sign of the charge is reversed?

A singly charged ion moves in a circle of radius \(0.20\,\mathrm{m}\) at speed \(4.0\times10^5\,\mathrm{m\,s^{-1}}\) in \(0.30\,\mathrm{T}\). Find its mass.

A charged particle has momentum \(p\) perpendicular to a magnetic field. Express its orbit radius in terms of \(p\).

Find the magnetic field needed for a proton moving at \(1.0\times10^6\,\mathrm{m\,s^{-1}}\) to have radius \(0.10\,\mathrm{m}\).

Why does the period not depend on speed for nonrelativistic circular motion in a uniform magnetic field?

A particle enters a magnetic field with kinetic energy doubled. How does the circular radius change if \(B\), \(m\), and \(|q|\) stay fixed?

A helical path has parallel speed \(v_\parallel\) and period \(T\). What is the pitch of the helix?

Derive the helical motion model for a charged particle entering a uniform magnetic field at an arbitrary angle.