20.3 Force on a moving charge

For charge q moving at speed v through field B, magnetic force magnitude is F=Bqv sinθ and direction is perpendicular to v and B.

Use the right-hand rule for positive charges and reverse the direction for negative charges. A stationary charge feels no magnetic force.

A charged particle entering perpendicular to a uniform field follows circular motion because the force continually turns its velocity.

Magnetic force does no work on an isolated moving charge because it is perpendicular to velocity, so speed stays constant.

A charge Q moving at speed v through magnetic field B feels force magnitude F=BQv sinθ, where θ is the angle between velocity and field.

Use the right-hand rule for a positive charge and reverse direction for a negative charge. The force is zero for parallel motion.

A charge entering perpendicular to B experiences maximum force and follows a circular path if no electric field acts.

Magnetic force depends on velocity direction, not simply speed; a stationary charge feels no magnetic force.

Moving charge carriers are deflected sideways by a magnetic field, building a transverse Hall voltage until electric and magnetic forces balance.

The sign and size depend on carrier type, current, field, thickness and orientation. At balance qE_H=qvB.

Reversing the magnetic field reverses Hall voltage, while increasing current increases the voltage for a fixed sample.

Hall voltage is not the ordinary voltage drop along the conductor; it is transverse to current.

A Hall probe uses a known current and Hall coefficient so measured transverse voltage can be converted to magnetic flux density.

Keep probe face orientation, current and calibration fixed; reverse or zero the probe to identify offsets and field direction.

A probe calibrated at 20 mV T⁻¹ giving 6 mV indicates B=0.30 T under the stated operating current.

A Hall probe does not directly measure force or electric potential of the source; it infers B from carrier deflection.

With velocity perpendicular to a uniform B, magnetic force provides centripetal force, so the particle follows circular motion with r=mv/(BQ).

Speed remains constant because magnetic force is perpendicular to velocity; reverse charge or field reverses curvature.

A faster particle follows a larger-radius path in the same field, while a more highly charged particle curves more tightly.

Magnetic field changes direction of velocity, not speed, and the path is helical if velocity has a component parallel to B.

In a velocity selector, electric and magnetic forces oppose. Particles pass undeflected when qE=qvB, so v=E/B.

This condition assumes perpendicular, uniform fields and the correct orientation; faster or slower particles deflect.

E=2.0×10⁴ N C⁻¹ and B=0.50 T select v=4.0×10⁴ m s⁻¹.

The selector does not select charge sign or mass directly; it selects speed, with curvature after the selector used for further analysis.