The electric-field case is the closest electromagnetic analogue to projectile motion. The force is constant in a uniform field, so the field component of motion has constant acceleration while any perpendicular component remains constant if no other force acts.

A charge q in a uniform electric field experiences force F = qE.

The acceleration is a = qE/m, so a uniform field gives uniform acceleration.

A positive charge accelerates in the direction of E; a negative charge accelerates opposite to E.

If the particle enters parallel to E, its speed changes along the field direction.

If it enters perpendicular to E, it keeps constant velocity perpendicular to E while accelerating along E, giving a parabolic path.

Label the motion features for charges in a uniform electric field.

Label

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4

Describe the motion of a charged particle entering a uniform electric field perpendicular to the field lines.

Calling the path circular or forgetting that negative charges deflect opposite to E.

Describe the motion of a charged particle entering a uniform electric field perpendicular to the field lines.

Choose

Magnetic-field motion is not like electric-field acceleration. A magnetic field can curve the path because the force is sideways, but it cannot speed the particle up or slow it down by itself.

A moving charge in a magnetic field experiences force F = qvB sinθ.

The magnetic force is perpendicular to both velocity and magnetic field.

Because the force is perpendicular to velocity, it does no work and does not change the particle’s speed.

If v is perpendicular to a uniform B field, the force provides centripetal force and the path is circular.

If v is parallel to B, sinθ = 0 and there is no magnetic force.

Label the magnetic-field motion diagram.

Label

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4

Explain why the speed of a charged particle does not change when it moves in a magnetic field.

Saying there is no force because speed is constant.

Explain why the speed of a charged particle does not change when it moves in a magnetic field.

Choose

A velocity selector is a force-balance device. The electric field tries to deflect the charge one way, the magnetic field the other. Only the speed that makes the two magnitudes equal passes straight through.

Crossed-field setups use perpendicular electric field, magnetic field, and particle velocity.

The electric force has magnitude qE; the magnetic force has magnitude qvB when v is perpendicular to B.

For a particle to pass straight through, the forces must be equal and opposite: qE = qvB.

The selected speed is v = E/B, independent of charge and mass.

Particles faster than E/B are deflected by the larger magnetic force; slower particles are deflected by the larger electric force, with direction depending on field orientation and charge sign.

Label the velocity-selector force balance.

Label

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5

Derive the selected speed for a particle passing undeflected through crossed electric and magnetic fields.

Leaving q or m in the final expression.

Derive the selected speed for a particle passing undeflected through crossed electric and magnetic fields.

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This card is the formula-and-direction anchor for D.3. The equation gives magnitude; the hand rule and charge sign give direction. Always check θ before assuming F = qvB.

The magnitude of magnetic force on a moving charge is F = |q|vB sinθ.

θ is the angle between velocity and magnetic field.

Force is maximum when v is perpendicular to B and zero when v is parallel to B.

The force direction is perpendicular to both v and B.

Use Fleming’s left-hand rule for conventional current or positive charge; reverse the direction for a negative charge.

Assemble F = qvB sinθ and the direction rule.

Formula

Target formula F = qvB sinθ

F

magnetic force magnitude

N

q

charge magnitude

C

v

particle speed

m s^-1

B

magnetic flux density

T

θ

angle between velocity and magnetic field

degrees or radians

1Use the magnetic-force magnitude.F = |q|vB sinθ

2Check the maximum-force case.θ = 90° -> F = |q|vB

3Check the zero-force case.θ = 0° -> F = 0

4Use the hand rule and charge sign.left-hand rule for positive charge; reverse for negative charge

Build the formula

A charged particle moves at angle θ to a magnetic field. State the magnetic force and explain when it is zero.

Omitting sinθ or giving the same direction for positive and negative charges.

A charged particle moves at angle θ to a magnetic field. State the magnetic force and explain when it is zero.

Choose

A wire feels a magnetic force because moving charges in the wire feel magnetic forces. In IB problems, use the macroscopic version F = BIL sinθ and then state the hand-rule direction.

A current-carrying conductor in a magnetic field experiences a force called the motor effect.

The force magnitude is F = BIL sinθ.

L is the length of conductor within the magnetic field, and θ is the angle between current and field.

The force is maximum when current is perpendicular to B and zero when current is parallel to B.

Use Fleming’s left-hand rule: first finger field, second finger current, thumb force.

Assemble the conductor-force model.

Formula

Target formula F = BIL sinθ

F

force on the conductor

N

B

magnetic flux density

T

I

current in the conductor

A

L

length of conductor in the field

m

θ

angle between current and magnetic field

degrees or radians

1Use the motor-effect magnitude.F = BIL sinθ

2Identify only the wire length inside the field.L = length in B field

3Check maximum force.θ = 90° -> F = BIL

4Use Fleming’s left-hand rule.first finger B, second finger I, thumb F

Build the formula

State the force on a current-carrying conductor in a magnetic field and how to determine its direction.

Using particle formula qvB for the whole wire or using length outside the field.

State the force on a current-carrying conductor in a magnetic field and how to determine its direction.

Choose

This model is a two-step idea wrapped into one formula: one current creates B, the other current in that B feels a force. The direction rule is simple for parallel wires: same currents attract, opposite currents repel.

Each long straight current-carrying wire produces a magnetic field that acts on the current in the other wire.

For two long parallel wires, force per unit length is F/L = μ0I1I2/(2πd).

d is the perpendicular separation between the wires.

Currents in the same direction attract each other.

Currents in opposite directions repel each other.

The forces on the two wires are equal in magnitude and opposite in direction.

Assemble the parallel-wire force model.

Formula

Target formula F/L = μ0I1I2/(2πd)

F/L

force per unit length

N m^-1

μ0

permeability of free space

T m A^-1

I1

current in first wire

A

I2

current in second wire

A

d

separation between wires

m

1Use the long-parallel-wire formula.F/L = μ0I1I2/(2πd)

2Predict force direction for same current direction.same direction currents attract

3Predict force direction for opposite current direction.opposite direction currents repel

4State the force pair relation.forces are equal and opposite

Build the formula

Two long parallel wires carry currents. State the force per unit length and the direction rule for same and opposite currents.

Saying same-direction currents repel or using d as wire length.

Two long parallel wires carry currents. State the force per unit length and the direction rule for same and opposite currents.

Choose

D.3 is a decision tree. Electric fields do work and can change speed. Magnetic fields exert perpendicular forces, bend paths, and produce circular motion when perpendicular to velocity. Wires use the current versions of the same magnetic-force ideas.

A charge in a uniform electric field feels F = qE and accelerates uniformly; perpendicular entry gives parabolic deflection.

A moving charge in a magnetic field feels F = qvB sinθ; the force is perpendicular to velocity and does no work.

For v perpendicular to uniform B, magnetic force provides centripetal force: qvB = mv^2/r, so r = mv/(qB) and T = 2πm/(qB).

In crossed fields, no deflection requires qE = qvB, so v = E/B.

A current-carrying conductor in a magnetic field experiences F = BIL sinθ.

Parallel currents exert F/L = μ0I1I2/(2πd); same direction currents attract and opposite currents repel.

Match each D.3 cue to its equation or direction rule.

Match

Reasons

0/8

Summarize how charged particles and currents move or experience forces in electromagnetic fields.

Listing equations without the angle, condition, or direction rule.

Summarize how charged particles and currents move or experience forces in electromagnetic fields.

Choose

IB Physics HL D.3 Motion in electromagnetic fields Notes

Map Charge in electric fields

Map Charge in magnetic fields

Map Crossed electric and magnetic fields

Map Magnetic force on charge

Map Force on current-carrying conductor

Analyze Force between parallel wires

Retrieve the D.3 Motion in electromagnetic fields Model