Magnetic force on charges and the velocity selector
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Question
What is the magnetic force on a moving charge?
Answer
**F = qvB** when the charge moves at right angles to the field B (given as F = qvB sinθ). It is **zero** for a stationary charge.
Question
Which way does the magnetic force on a moving charge point?
Answer
**Perpendicular** to the velocity v (and to B). Because it is always sideways, it changes the charge's **direction** but never its **speed**.
Question
Why does a charge follow a circle in a uniform magnetic field?
Answer
The force F = qvB is always perpendicular to v, so it acts as a **centripetal force**, curving the path into a **circle** of radius r = mv/(qB).
Question
Formula for the radius of a charge's circular path in a magnetic field?
Answer
$r = \dfrac{mv}{qB}$ — a heavier or faster particle curves in a bigger circle; a stronger field or bigger charge curves it tighter.
Question
What is a velocity selector?
Answer
A device with **crossed** electric and magnetic fields (E and B at right angles). Only charges of one speed pass straight through; the rest are deflected.
Question
What is the condition for a charge to pass straight through a velocity selector?
Answer
The electric and magnetic forces **balance**: **qE = qvB**. The net force is then zero, so the charge is undeflected.
Question
What speed is selected by a velocity selector?
Answer
$v = \dfrac{E}{B}$ — from qE = qvB, the charge q cancels.
Question
Does the selected speed v = E/B depend on the charge or mass?
Answer
**No** — q cancels in qE = qvB, so every undeflected particle has the same speed v = E ÷ B, whatever its charge or mass.
Question
In a velocity selector, what happens to a charge moving SLOWER than v = E/B?
Answer
The magnetic force qvB is smaller, so the **electric force qE wins** and the charge is deflected the way qE points.
Question
In a velocity selector, what happens to a charge moving FASTER than v = E/B?
Answer
The magnetic force qvB is larger, so the **magnetic force wins** and the charge is deflected the other way.
Question
A selector has E = 2.0 × 10⁴ N C⁻¹ and B = 0.10 T. What speed passes through?
Answer
v = E ÷ B = (2.0 × 10⁴) ÷ 0.10 = 2.0 × 10⁵ m s⁻¹.
Question
Why does a magnetic field never change a charge's kinetic energy?
Answer
The force is perpendicular to the motion, so it does **no work** on the charge — only its direction changes, not its speed.
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Full study notes for Magnetic force on charges and the velocity selector
Topic 4.3 hub
Motion in electromagnetic fields
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