NDA Physics · Electricity and Magnetism

Magnetic Force and Fleming's Rules

A magnetic field pushes on a moving charge (F = qvB sinθ) and on a current-carrying wire (F = BIL); the force is perpendicular to both, zero when motion is along the field, and its direction is found with Fleming's left-hand rule (motor) or right-hand rule (generator).

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Why this matters

Five PYQs, and a reliable source of direction-trap questions. The essentials: the force on a moving charge is greatest when it crosses the field at right angles and zero when it moves along the field; positive and negative charges deflect opposite ways; and the two Fleming's rules — LEFT hand for the force on a current (motor), RIGHT hand for the current induced by motion (generator).

Concept 1 of 3

Force on a charge moving in a magnetic field

Intuition

A magnetic field only pushes on a charge that is MOVING, and only on the part of the motion that crosses the field. Move straight along the field and you feel nothing; cross it at right angles and the push is maximum. The force is always sideways — perpendicular to both the velocity and the field.

Definition

The magnetic force on a charge $q$ moving with speed $v$ at angle $\theta$ to a field $B$ is ** $F = qvB\sin\theta$ **, directed perpendicular to both $v$ and $B$ .

Maximum ( $F = qvB$ ) when $v \perp B$ ( $\theta = 90°$ ).
Zero when $v \parallel B$ or antiparallel ( $\theta = 0°$ or $180°$ ).

Positive and negative charges feel forces in opposite directions, so a beam of mixed charge separates.

Magnetic force on a moving charge

F = qvB\sin\theta

qcharge (C)
vspeed (m/s)
Bmagnetic field (T)
\thetaangle between v and B

Diagram · drag to rotate F = qv × B

v, B and F = qv × B are mutually perpendicular. When v ⊥ B the charge circles in the plane perpendicular to B, with F pointing to the centre. If v ∥ B, F = 0 and it goes straight.

Worked example

A proton moves parallel to a uniform magnetic field. What magnetic force does it experience?

$F = qvB\sin\theta$ with $\theta = 0°$ (motion along the field).
$\sin 0° = 0$ .
So the force is zero — a charge moving along the field feels no magnetic force.

Answer:Zero — there is no force when the velocity is parallel to B.

Practice this conceptself-check · 3 quick reps

Try it yourself

A positive charge moves toward the south; the magnetic field points toward the north. What force does it feel?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
When is the magnetic force on a moving charge maximum?
2.
Force on a charge moving along the field direction?
3.
Do positive and negative charges deflect the same way in a magnetic field?

From the bank · past-year question

Example 1Electricity and MagnetismMODERATE

A positive charge is moving towards south in a space where magnetic field is pointing in the north direction. The moving charge will experience :

[Q89 · Apr · 2023]

No force when motion is ALONG (or against) the field

Both θ = 0° and θ = 180° give sinθ = 0, so a charge moving parallel OR antiparallel to B feels no magnetic force. 'Moving south, field north' is the antiparallel case — the answer is no deflecting force, not a sideways one.

Drill 2 more on force on a charge moving in a magnetic field

Concept 2 of 3

Force on a current-carrying conductor — Fleming's left-hand rule

Intuition

A wire carrying current in a magnetic field is really a stream of moving charges, so the field pushes on it too. The force is F = BIL, and its DIRECTION comes from Fleming's LEFT-hand rule — the rule behind every electric motor.

Definition

A straight conductor of length $L$ carrying current $I$ across a field $B$ feels a force ** $F = BIL$ ** (when $B \perp I$ ), perpendicular to both. Fleming's left-hand rule (motor rule): hold the left hand with thumb, forefinger and middle finger mutually perpendicular —

Forefinger → Field (B),
Centre finger → Current (I),
Thumb → Thrust (force/motion).

Force on a current-carrying conductor

F = B I L

Fforce (N)
Bmagnetic field (T)
Icurrent (A)
Llength of conductor in the field (m)

Diagram · drag to rotate Fleming's left hand

Left hand, three fingers at right angles: Fore-finger = Field, Centre-finger = Current, Thumb = Thrust (force). Drag to confirm all three stay mutually perpendicular — this is the motor rule.

Worked example

Which rule gives the direction of the force on a straight current-carrying conductor placed perpendicular to a magnetic field?

The force on a current in a field is the MOTOR effect.
Its direction comes from Fleming's LEFT-hand rule.
(Forefinger = field, centre finger = current, thumb = force.)

Answer:Fleming's left-hand rule.

Practice this conceptself-check · 3 quick reps

Try it yourself

A conductor of length 0.5 m carries 4 A perpendicular to a 0.2 T field. What is the force on it?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Which Fleming's rule gives the force on a current-carrying conductor?
2.
In Fleming's left-hand rule, the thumb represents…
3.
Force on a 2 m wire carrying 3 A across a 0.1 T field?

From the bank · past-year question

Example 2Electricity and MagnetismEASY

The rule to determine the direction of a force experienced by a straight current carrying conductor placed in a magnetic field which is perpendicular to it is

[Q52 · Sep · 2025]

LEFT hand for force (motor), not right

Fleming's LEFT-hand rule gives the FORCE on a current (motor effect). The right-hand rule is for the current INDUCED by motion (generator). The distractor 'right-hand rule' is the classic swap.

Concept 3 of 3

Induced current — Fleming's right-hand rule

Intuition

Run the motor backwards: instead of current making a wire move, MOVE a wire through a field and it generates a current. That's a generator, and the direction of the induced current comes from Fleming's RIGHT-hand rule.

Definition

When a conductor is moved through a magnetic field, an EMF (and current) is induced. Fleming's right-hand rule (generator/dynamo rule): with the right hand's thumb, forefinger and middle finger mutually perpendicular —

Forefinger → Field (B),
Thumb → motion of the conductor,
Centre finger → induced current.

Worked example

By Fleming's right-hand rule, the forefinger points along the magnetic field and the thumb along the motion of the conductor. What does the stretched middle finger give?

Fleming's right-hand rule is the GENERATOR rule.
Forefinger = field, thumb = motion (input).
The middle finger then gives the INDUCED current (output).

Answer:The direction of the induced current.

Practice this conceptself-check · 3 quick reps

Try it yourself

Which device works on the rule that moving a conductor through a magnetic field induces a current — and which Fleming's rule applies?

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
Which Fleming's rule gives the direction of induced current?
2.
Fleming's right-hand rule is associated with which machine?
3.
In Fleming's right-hand rule, the middle finger represents…

From the bank · past-year question

Example 3Electricity and MagnetismMODERATE

According to Fleming's right-hand rule, if the forefinger indicates the direction of magnetic field and thumb shows the direction of motion of conductor, then the stretched middle finger will predict the direction of

[Q96 · Apr · 2022]

Right hand → induced current (generator)

Keep the pair straight: LEFT hand = force on a current (motor), RIGHT hand = current induced by motion (generator). Here forefinger = field and thumb = motion, so the middle finger gives the INDUCED CURRENT — not 'force' and not 'electric field'.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Force on a charge moving in a magnetic field
Magnetic force on a moving charge
$F = qvB\sin\theta$
Force on a current-carrying conductor — Fleming's left-hand rule
Force on a current-carrying conductor
$F = B I L$

Watch out for (3)

No force when motion is ALONG (or against) the field
→ Force on a charge moving in a magnetic field
LEFT hand for force (motor), not right
→ Force on a current-carrying conductor — Fleming's left-hand rule
Right hand → induced current (generator)
→ Induced current — Fleming's right-hand rule

Mastery check — 2 interleaved questions

Try each one before clicking. Questions are interleaved across the concepts above, not grouped — interleaving sharpens transfer.

Example 1Electricity and MagnetismHARD

A proton enters a magnetic field at right angles to it, as shown above. The direction of force acting on the proton will be

[Q132 · Apr · 2020]

Example 2Electricity and MagnetismHARD

What will happen if a collection of positive and negative charges are passed at a high speed through a magnetic field which is perpendicular to the direction of motion of the charges? (Assume that both kind of charges are NOT going to recombine)

[Q110 · Sep · 2023]

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