Force on a current-carrying conductor in a magnetic field

The basic fact. When a straight conductor carrying a current is placed inside a magnetic field, and the current direction is not parallel to the field direction, the conductor experiences a force. This was discovered experimentally, long before anyone could write down a formula for it, and it is the reason electricity can be turned into motion.

Direction — Fleming's Left-Hand Rule. Hold out the thumb, forefinger, and middle finger of your left hand so that all three are mutually perpendicular — like three edges meeting at the corner of a box. Then:

• Forefinger → direction of the magnetic field.
• Middle finger → direction of the current.
• Thumb → direction of the force (and hence the motion) on the conductor.

A quick mnemonic locks the order in: Forefinger–Field, seCond (middle) finger–Current, thuMb–Motion. It is easy to reach for the right hand out of habit, because the right-hand thumb rule appeared earlier in this chapter — but that rule answers a different question (which way does a current's own field curl). Here the field already exists from outside, and we want the force on a wire sitting inside it, so it is strictly the left hand.

What makes the force bigger or smaller. No formula is needed at Class 10 level — only the qualitative trend, and it is worth stating precisely:

• The force increases as the current increases.
• The force increases as the magnetic field strength increases.
• The force increases as the length of conductor lying inside the field increases.
• The force is maximum when the current is perpendicular to the field, shrinks as the angle between them departs from a right angle, and falls to zero when the current is exactly parallel to the field.

Why this matters — the electric motor. A rectangular coil carrying current, placed between the poles of a magnet, has its two long sides carrying current in opposite directions (because the current goes around the loop). Fleming's Left-Hand Rule then gives opposite force directions on the two sides — one side is pushed up while the other is pushed down. Two equal, opposite forces acting on opposite sides of a coil form a turning effect (a couple), and that couple rotates the coil. A split-ring commutator reverses the current every half-turn so the couple keeps acting in the same rotational sense, and the coil spins continuously. That is the electric motor, in outline; it is treated only lightly this cycle, and the force rule above is the part you are actually examined on.

The force on a current-carrying conductor in a magnetic field is not something you can derive from Ohm's law or Coulomb's law at this stage — at Class 10 it is presented as an experimental fact, backed by a specific hands-on demonstration, and Fleming's Left-Hand Rule is simply a convenient bookkeeping device for a direction that was measured, not calculated, so the goal here is to understand why the rule works the way it does and why the special angles behave as they do, using only the ideas already in the syllabus.

Step 1. Picture the standard classroom demonstration: a straight, flexible wire is hung between the poles of a strong horseshoe magnet (so the field points from the north pole to the south pole, roughly horizontal), and the wire itself is connected to a battery and a switch so current can be sent through it, either left-to-right or right-to-left. The wire is otherwise free to swing.

Step 2. Close the switch. The wire visibly kicks — it jumps sideways, in a direction perpendicular to both itself and the magnetic field, and stays deflected as long as the current flows. Reverse the battery connections so the current flows the opposite way, and the wire kicks to the opposite side. This reversal is the key experimental clue: the force direction depends on the current direction, not just its presence.

Step 3. Now rotate the horseshoe magnet 90 degrees so its field direction changes while the current direction stays the same. The wire's deflection direction changes too — the force also depends on the field direction, and it always comes out perpendicular to both the current and the field, never along either of them. Fleming's Left-Hand Rule is nothing more than a memory aid that encodes exactly this observed perpendicularity: forefinger and middle finger set the two given directions, and the thumb — automatically perpendicular to both once the hand is held correctly — reads off the force direction without needing any calculation.

Step 4. Finally, slowly rotate the wire itself so the angle between the current and the field changes continuously. The kick is strongest when the wire is held at right angles to the field, weakens as the wire is tilted toward the field direction, and vanishes completely the moment the wire lies exactly parallel to the field. This is consistent with the rule: current parallel to field is the one configuration where the "middle finger along current, forefinger along field" instruction from Step 3 cannot be satisfied while keeping the fingers mutually perpendicular in a meaningful way — physically, a current running along the field lines has no component of current across the field to be pushed on, so there is nothing for the field to act on sideways, and the force is zero.

A straight conductor carries current toward the east, lying in a magnetic field that points vertically upward, out of the ground. Find the direction of the force on the conductor, and then state what happens to that force if the same conductor is instead turned so that its current flows due north — straight along a horizontal compass direction — while the field stays vertically upward.

Step 1. Set up the left hand with thumb, forefinger, and middle finger mutually perpendicular, ready to represent force, field, and current respectively.

Step 2. Point the forefinger in the field direction, vertically upward, and the middle finger in the current direction, toward the east. Holding the hand in this configuration, the thumb — perpendicular to both — settles along the horizontal north–south line, and working through the geometry, it points toward the south.

Step 3. For the second part, the field is still exactly vertical, and the current is now due north — still horizontal, and still perpendicular to the vertical field, since a horizontal direction and a vertical direction are always at right angles to each other. The angle between current and field has not changed (it is still $90^\circ$), only the compass direction of the current has changed, so the force is still present and still at its maximum possible strength for this current and field — it has simply rotated in direction along with the current. Applying the rule again (forefinger up, middle finger north) gives the new force direction pointing due west.

Answer: with current east and field vertically upward, the force acts due south; turning the current to due north (field unchanged) swings the force to due west, with its strength unchanged because the current is still perpendicular to the field in both cases.

• Reaching for the right hand out of exam-hall habit — Fleming's Left-Hand Rule specifically needs the left hand; the right-hand thumb rule from earlier in the chapter answers a different question (the field made by a current) and uses the right hand instead.
• Mixing up which finger is which — Field goes on the forefinger, Current on the second (middle) finger, and Motion/force on the thuMb; get the order wrong and the answer rotates to a wrong axis.
• Assuming the force is always at its maximum — it is only maximum when current and field are exactly perpendicular; at other angles it is smaller, and many students forget the angle matters at all.
• Assuming current-in-a-field always means a force — if the current is exactly parallel (or antiparallel) to the field, there is no sideways push at all, and the force is zero regardless of how large the current or field is.

Ask the tutor: if you keep mixing up the left-hand and right-hand rules under pressure, ask the AI tutor for a rapid-fire set of current-and-field direction problems to drill the difference until it is automatic.