The big idea: A moving charge in a magnetic field feels a force: F = qvB (when the charge moves at right angles to the field).
This force is always perpendicular to the velocity — it pushes the charge sideways, never forwards or backwards.
A constant sideways push bends the path into a circle.
Magnetic force on a moving charge
- Size: F = qvB (when v is perpendicular to B)
- Direction: perpendicular to the velocity v — always sideways
- A sideways push can't speed it up or slow it down, so it bends the path into a circle of radius r = mv/(qB)
Electric force on a charge (for contrast)
- Size: F = qE (in a field E)
- Direction: along the field — parallel to E
- A push along the motion changes the speed (it can speed up or slow the charge)
Spot it: Stationary charge → no magnetic force (you need v).
The force is sideways, so it can't change the speed — only the direction, curving the charge into a circle.
The data booklet gives the magnetic force on a moving charge. For a charge moving at right angles to the field (the case the exam tests):
- magnetic force on the charge (N)
- size of the moving charge (C)
- speed of the charge (m s⁻¹)
- magnetic field strength (T, tesla)
What a velocity selector is: A velocity selector sends charges through crossed fields — an electric field E and a magnetic field B at right angles to each other.
The electric force qE pushes one way; the magnetic force qvB pushes the opposite way. Only charges of one exact speed feel zero net force and pass straight through.
[Diagram: phys-field-lines] - Available in full study mode
[Diagram: phys-free-body] - Available in full study mode
For the charge to go straight (undeflected) the two forces must be equal. Set them equal and the charge q cancels:
- selected speed — the speed that passes straight through (m s⁻¹)
- electric field strength between the plates (N C⁻¹ or V m⁻¹)
- magnetic field strength (T)
[Diagram: phys-formula-triangle] - Available in full study mode
Worked example — the selected speed
A velocity selector has an electric field of E = 3.0 × 10⁴ N C⁻¹ and a magnetic field of B = 0.20 T, crossed at right angles. Find the speed of a charge that passes straight through undeflected.
Solution
- Undeflected means the forces balance — start with the given condition:
- Cancel q and rearrange to make v the subject:
- Put in the numbers (E = 3.0 × 10⁴, B = 0.20):
- Work it out — keep the unit:
Final answer
v = 1.5 × 10⁵ m s⁻¹ — and this is the same for any charge, whatever its size or mass.
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How this is tested: The velocity selector is a classic Paper-2 'crossed fields' question.
- Paper 2: a particle passes undeflected through crossed fields — you find the magnetic field B (or E, or the speed v) from the balance qE = qvB. - Paper 2: then a different charge enters the same fields at the same speed — you draw or describe its path (it curves, because the magnetic force qvB now changes).
Classic trap: thinking the selected speed depends on the charge or mass — it doesn't. v = E ÷ B only.
A different particle deflects: Set B by balancing one particle. A second particle of a different charge or mass moving at a different speed no longer satisfies qE = qvB, so one force wins and it curves.
Slower than v = E/B
- Magnetic force qvB is smaller (v is smaller)
- Electric force qE now wins
- The charge is deflected toward the − plate (the way qE points)
Faster than v = E/B
- Magnetic force qvB is larger (v is larger)
- Magnetic force now wins
- The charge is deflected the other way (the way qvB points)
IB-style question — (a) the magnetic field for no deflection
An electron enters a velocity selector at 4.0 × 10⁶ m s⁻¹. The electric field between the plates is E = 8.0 × 10⁵ N C⁻¹. Find the magnetic field strength B that lets the electron pass through undeflected.
Solution
- Undeflected ⇒ the electric and magnetic forces balance:
- Cancel q and make B the subject:
- Put in the numbers (E = 8.0 × 10⁵, v = 4.0 × 10⁶):
- Work it out — keep the unit:
Final answer
B = 0.20 T. (Notice the electron's charge never enters the answer — it cancelled.)
IB-style question — (b) a faster electron
A second electron enters the same crossed fields, but moving faster than 4.0 × 10⁶ m s⁻¹. State whether it passes straight through, and which force wins.
Solution
- The electric force qE does not depend on speed, but the magnetic force qvB grows with v.
- A faster electron makes qvB larger than qE, so the forces no longer balance.
- The magnetic force wins, so the electron is deflected (it does not pass straight through).
Final answer
It is deflected — moving faster makes the magnetic force qvB bigger than the electric force qE, so the magnetic force wins.