The Velocity Selector | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

The Velocity Selector

An electric field and a magnetic field can act on the same charged particle in opposite directions.

Only one speed makes the two force magnitudes equal. Particles at that speed pass straight through.

Balance the two forces

Swipe left or right to see the whole diagram →

Crossed fields: the electric force |q|E is fixed; the magnetic force B|q|v grows with speed. Only particles with v = E/B feel balanced forces and pass straight through.

An undeviated particle has no resultant force, so the electric and magnetic force magnitudes are equal.
$|q|E=B|q|v$
The charge magnitude cancels.
$v=\dfrac{E}{B}$
For parallel plates, use the potential difference and plate separation.
$E=\dfrac{V}{d} \qquad\Longrightarrow\qquad v=\dfrac{V}{Bd}$

The selected speed does not depend on particle mass or charge.

What happens at the wrong speed

Swipe left or right to see the whole diagram →

The electric force is fixed, but the magnetic force grows with speed. Fast: magnetic force wins. Selected speed: the forces balance. Slow: electric force wins.

The electric force does not depend on speed.
The magnetic force increases with speed.
A faster positive ion in the shown arrangement curves toward the magnetic-force side. A slower ion curves toward the electric-force side.

Your turnquick check

A particle moves faster than the selected speed. Which force is now larger: electric or magnetic?

Show worked answer

The magnetic force is larger because it increases with speed.

The Velocity Selector

An electric field and a magnetic field can act on the same charged particle in opposite directions.

Only one speed makes the two force magnitudes equal. Particles at that speed pass straight through.

Balance the two forces

Swipe left or right to see the whole diagram →

Crossed fields: the electric force |q|E is fixed; the magnetic force B|q|v grows with speed. Only particles with v = E/B feel balanced forces and pass straight through.

An undeviated particle has no resultant force, so the electric and magnetic force magnitudes are equal.
$|q|E=B|q|v$
The charge magnitude cancels.
$v=\dfrac{E}{B}$
For parallel plates, use the potential difference and plate separation.
$E=\dfrac{V}{d} \qquad\Longrightarrow\qquad v=\dfrac{V}{Bd}$

The selected speed does not depend on particle mass or charge.

What happens at the wrong speed

Swipe left or right to see the whole diagram →

The electric force is fixed, but the magnetic force grows with speed. Fast: magnetic force wins. Selected speed: the forces balance. Slow: electric force wins.

The electric force does not depend on speed.
The magnetic force increases with speed.
A faster positive ion in the shown arrangement curves toward the magnetic-force side. A slower ion curves toward the electric-force side.

Your turnquick check

A particle moves faster than the selected speed. Which force is now larger: electric or magnetic?

Show worked answer

The magnetic force is larger because it increases with speed.