TORQUE EXPERIENCED BY A CURRENT LOOP IN A UNIFORM MAGNETIC FIELD

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BOARD: CBSE and SEBA Assam

SUBJECT: Physics

TOPIC: Torque on a current loop in a uniform magnetic field

Torque on a current loop in a uniform magnetic field

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TORQUE ON A CURRENT LOOP IN A UNIFORM MAGNETIC FIELD

What exactly makes the loop rotate in a magnetic field?

Two equal and opposite magnetic forces act on opposite sides of the loop forming a couple → producing torque.

🧠 Think Like This First: Magnetic field does NOT push the whole loop forward. It twists it. Field tries to rotate and align the loop.

STEP 1: VISUALISING THE RECTANGULAR COIL

Consider rectangular coil PQRS:

1. Current I flows through the loop.
2. Sides = a and b
3. Area A = ab
4. Magnetic field = B
5. Angle between B and normal to coil = θ

Direction of the area and B makes an angle θ

🧠 Important: Always think in terms of the normal to the plane. That normal direction is the direction of magnetic moment.

STEP 2: APPLY MAGNETIC FORCE LAW

Force on a current carrying conductor: F = I (L × B)

Using Fleming’s Left Hand Rule:

1. Side QR → Force upward → F₁ = IaB
2. Side SP → Force downward → F₁′ = IaB

These two cancel each other → Net vertical force = 0

🧠 First Clarity: No net force. So the loop does NOT move up or down. It rotates.

STEP 3: FORCES RESPONSIBLE FOR ROTATION

Now observe other two sides:

1. Side SR → Force coming out of page → F = IbB
2. Side QP → Force going into page → F′ = IbB

These forces are:

• Equal
• Opposite
• Parallel
• Separated by distance “a”

Such forces form a Couple → producing torque.

🧠 Couple = Rotation Generator No translation, only twisting.

STEP 4: CALCULATION OF TORQUE

Torque = Force × Perpendicular distance Here:

• Force = IbB
• Distance = a sinθ

So, τ = F × a sinθ τ = IbB × a sinθ

τ = I B A sinθ Since A = ab

FOR N TURNS OF COIL

If there are N turns, τ = N I B A sinθ

Why multiply by N? Each turn experiences same torque. Total torque = Sum of all torques.

🧠 More turns → More torque → Stronger rotation This is the working principle of an electric motor.

MAGNETIC MOMENT CONCEPT (DEEP THINKING)

Magnetic moment: m = N I A Torque becomes: τ = m B sinθ

Vector form: τ = m × B

🧠 Ultimate Understanding: Current loop behaves like a tiny bar magnet. Magnetic field tries to align magnetic moment with itself.

WHEN IS TORQUE ZERO?

When θ = 0:

• sinθ = 0
• τ = 0

This happens when: Plane of loop ⟂ Magnetic field (Normal parallel to B)

🧠 Already aligned → No rotation needed.

WHEN IS TORQUE MAXIMUM?

When θ = 90°:

• sinθ = 1
• τ = NIBA (maximum)

This happens when: Plane of loop ∥ Magnetic field

🧠 Maximum misalignment → Maximum rotation force.

DIRECTION OF TORQUE

Using right-hand rule: Magnetic field tries to rotate loop so that magnetic moment aligns with B.

🧠 Nature Rule: Every dipole tries to align with the field. Misalignment creates torque. Alignment gives stability.

FINAL EXAM MEMORY COMPRESSION

τ = N I B A sinθ

🧠 Mental Flow Chart: Current → Magnetic Force Opposite Forces → Couple Couple → Torque Torque ∝ N, I, B, A, sinθ If you remember the “alignment story”, you will never forget the formula.

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