9702 · 20.3
Force on a moving charge flashcards
Revision flashcards for Cambridge 9702 Force on a moving charge (syllabus 20.3). Flip, recall, then mark a real past-paper question.
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What causes a charged particle to experience a magnetic force?
It experiences a magnetic force when it moves through a magnetic field, provided its velocity has a component perpendicular to the field.
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State the formula for the magnetic force on a single charged particle in a magnetic field.
$F = BQv\sin\theta$, where $\theta$ is the angle between velocity (v) and magnetic field (B).
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When is the magnetic force on a moving charge zero?
When the particle moves parallel ($\theta=0^\circ$) or anti-parallel ($\theta=180^\circ$) to the magnetic field lines.
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How do you determine the direction of the magnetic force on a *positive* charge?
Using Fleming's Left-Hand Rule: Thumb = Force, Forefinger = Magnetic Field, Middle Finger = Velocity/Motion.
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How does Fleming's Left-Hand Rule apply to *negative* charges?
The predicted force direction is opposite to that for a positive charge, or the middle finger points opposite to the actual velocity.
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What type of path does a charged particle take if it moves perpendicular to a uniform magnetic field?
It follows a circular path, as the magnetic force provides the necessary centripetal force.
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What is the purpose of a velocity selector?
To allow only charged particles moving at a specific velocity to pass through undeflected by balancing electric and magnetic forces.
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State the formula for the selected velocity in a velocity selector.
$v = E/B$, where E is the electric field strength and B is the magnetic flux density.
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Define the Hall effect.
The generation of a potential difference (Hall voltage) across a current-carrying conductor placed in a perpendicular magnetic field, due to charge carrier accumulation.
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What is a Hall probe used for?
To measure the magnetic flux density (B) by exploiting the Hall effect and measuring the Hall voltage produced.
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What factors influence the magnitude of the Hall voltage ($V_H$)?
Magnetic flux density (B), current (I), charge carrier number density (n), charge of one carrier (Q), and thickness of the conductor (t).
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What is the relationship between magnetic force and centripetal force for a charge moving perpendicularly in a uniform B-field?
The magnetic force provides the centripetal force, causing circular motion. The relationship is $BQv = \frac{mv^2}{r}$.
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Why does the magnetic force do no work on a charged particle?
Because the force is always perpendicular to the particle's velocity (and thus its displacement). Work done is $W = Fd\cos\theta$, and since the angle between force and displacement is $90^\circ$, $\cos(90^\circ) = 0$. This means the particle's kinetic energy and speed remain constant.
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What is the formula for the radius of the circular path of a charge in a uniform magnetic field?
$r = \frac{mv}{BQ}$
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How is the Hall voltage related to the thickness of the conductor?
The Hall voltage ($V_H$) is inversely proportional to the thickness ($t$) of the conductor. Thinner conductors produce a larger Hall voltage for the same magnetic field, current, and material.