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

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)
$\theta$ angle 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?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

NDA · Apr 2023 · Q89Moderate

Example 1 · Electricity and Magnetism · Magnetic Force and Fleming's Rules

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

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

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?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

NDA · Sep 2025 · Q52Easy

Example 2 · Electricity and Magnetism · Magnetic Force and Fleming's Rules

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

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

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?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

NDA · Apr 2022 · Q96Moderate

Example 3 · Electricity and Magnetism · Magnetic Force and Fleming's Rules

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

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

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