IB Physics Topic D.3.2 Charged Particle Motion in Magnetic Fields Revision Notes (SL/HL)

IB Physics Topic D.3.2 Charged Particle Motion in Magnetic Fields Revision Notes (SL/HL) | RevisionDojo

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Circular Motion of Charged Particles in a Magnetic Field

When a charged particle moves through a uniform magnetic field with its velocity perpendicular to the field, it experiences a magnetic force $F = qvB$.
This is the $\theta = 90^\circ$ case of the general law $F = qvB\sin\theta$ introduced in D.3.3, and the force is always perpendicular to both the velocity and the magnetic field.
This force acts as a centripetal force, causing the particle to move in a circular path.
Because this force is always perpendicular to the velocity, it does no work on the particle.
Its speed and kinetic energy stay constant; only the direction of the velocity changes.
A magnetic field can steer a charged particle but never speed it up or slow it down.

Deriving the Radius of the Circular Path

For this perpendicular case, the magnetic force has magnitude: $$F = qvB$$ where:
1. $q$ is the charge of the particle.
2. $v$ is the velocity of the particle.
3. $B$ is the magnetic field strength.
This force provides the centripetal force required to keep the particle in a circular path: $$F = \frac{mv^2}{r}$$
Equating the two expressions for force: $$qvB = \frac{mv^2}{r}$$
Solving for the radius $r$: $$r = \frac{mv}{qB}$$

Hint

The radius of the circular path depends on the particle’s mass, velocity, charge, and magnetic field strength.

Time for One Revolution

The time $T$ for the particle to complete one full revolution is: $$T = \frac{2\pi r}{v}$$
Substituting the expression for $r$: $$T = \frac{2\pi}{v} \cdot \frac{mv}{qB} = \frac{2\pi m}{qB}$$

Tip

The time for one revolution is independent of the particle’s speed.
This property is crucial in devices like cyclotrons.

Helical Motion: Combination of Circular and Linear Motion

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Circular Motion of Charged Particles in a Magnetic Field

When a charged particle moves through a uniform magnetic field with its velocity perpendicular to the field, it experiences a magnetic force $F = qvB$.
This is the $\theta = 90^\circ$ case of the general law $F = qvB\sin\theta$ introduced in D.3.3, and the force is always perpendicular to both the velocity and the magnetic field.
This force acts as a centripetal force, causing the particle to move in a circular path.
Because this force is always perpendicular to the velocity, it does no work on the particle.
Its speed and kinetic energy stay constant; only the direction of the velocity changes.
A magnetic field can steer a charged particle but never speed it up or slow it down.

Deriving the Radius of the Circular Path

For this perpendicular case, the magnetic force has magnitude: $$F = qvB$$ where:
1. $q$ is the charge of the particle.
2. $v$ is the velocity of the particle.
3. $B$ is the magnetic field strength.
This force provides the centripetal force required to keep the particle in a circular path: $$F = \frac{mv^2}{r}$$
Equating the two expressions for force: $$qvB = \frac{mv^2}{r}$$
Solving for the radius $r$: $$r = \frac{mv}{qB}$$

Hint

The radius of the circular path depends on the particle’s mass, velocity, charge, and magnetic field strength.

Time for One Revolution

The time $T$ for the particle to complete one full revolution is: $$T = \frac{2\pi r}{v}$$
Substituting the expression for $r$: $$T = \frac{2\pi}{v} \cdot \frac{mv}{qB} = \frac{2\pi m}{qB}$$

Tip

The time for one revolution is independent of the particle’s speed.
This property is crucial in devices like cyclotrons.

Helical Motion: Combination of Circular and Linear Motion

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Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

IB Physics D.3.2 Charged Particle Motion in Magnetic Fields Notes

Topic A - Space, time and motion5 subtopics

Topic B - The particulate nature of matter5 subtopics

Topic C - Wave behaviour5 subtopics

Topic D - Fields4 subtopics

Topic E - Nuclear and quantum physics5 subtopics

Circular Motion of Charged Particles in a Magnetic Field

Deriving the Radius of the Circular Path

Time for One Revolution

Helical Motion: Combination of Circular and Linear Motion

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Circular Motion of Charged Particles in a Magnetic Field

Deriving the Radius of the Circular Path

Time for One Revolution

Helical Motion: Combination of Circular and Linear Motion

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