Physics · Class 12 · Electromagnetism and Induction · Term 1

Torque on a Current Loop and Moving Coil Galvanometer

Students will analyze the torque experienced by a current loop in a magnetic field and the working of a galvanometer.

• CBSE Learning Outcomes
• CBSE: Moving Charges and Magnetism - Class 12

About This Topic

Students analyse the torque on a current-carrying loop in a uniform magnetic field, expressed as τ = N I A B sinθ, where N is turns, I current, A area, B field strength, and θ the angle between magnetic moment and field. They predict torque variations with loop orientation, maximum when the plane is parallel to field lines, causing rotation to align perpendicularly. This force drives devices like motors.

The moving coil galvanometer applies this principle: a lightweight coil in radial field deflects proportional to current until suspension fibre provides equal restoring torque, yielding θ = (N B A / k) I. Students learn conversions, adding shunt for ammeter to bypass excess current or series resistance for voltmeter to limit current, adjusting range while preserving sensitivity. These align with CBSE standards in Moving Charges and Magnetism.

Active learning suits this topic well. Students build coil models with batteries and magnets to measure deflections, compare predictions to observations, and design conversion circuits. Such hands-on work makes vector torque and instrument principles concrete, strengthens problem-solving, and connects theory to lab practice.

Key Questions

1. Predict how the torque on a current loop changes with the orientation of the loop in a magnetic field.
2. Explain the principle behind the operation of a moving coil galvanometer.
3. Design a method to convert a galvanometer into an ammeter or a voltmeter.

Learning Objectives

• Calculate the torque on a current loop in a uniform magnetic field for various orientations.
• Explain the principle of operation of a moving coil galvanometer based on torque balance.
• Compare the magnetic field patterns produced by a current loop and a bar magnet.
• Design a circuit modification to convert a galvanometer into an ammeter with a specific range.
• Analyze the effect of changing the angle between the magnetic moment and the magnetic field on the torque experienced by a current loop.

Before You Start

Magnetic Field due to a Current

Why: Students need to understand how currents create magnetic fields to analyze the interaction between a loop's field and an external field.

Force on a Current-Carrying Conductor in a Magnetic Field

Why: This is the foundational concept leading to the understanding of torque on a loop, which is essentially the net effect of forces on different parts of the loop.

Vector Cross Product

Why: Understanding the vector nature of magnetic moment and magnetic field, and their cross product for torque, is essential for a complete analysis.

Key Vocabulary

Magnetic dipole moment	A measure of an object's tendency to align with a magnetic field, for a current loop it is given by NIA, where N is the number of turns, I is the current, and A is the area of the loop.
Torque	A twisting force that tends to cause rotation. In this context, it's the force that rotates the current loop in a magnetic field.
Radial Magnetic Field	A magnetic field that is directed radially outward from or inward toward a central axis. In a galvanometer, this ensures the torque is proportional to the current, regardless of coil orientation.
Shunt Resistance	A low resistance connected in parallel with a galvanometer to divert most of the current, allowing it to function as an ammeter.
Series Resistance	A high resistance connected in series with a galvanometer to limit the current flowing through it, enabling it to function as a voltmeter.

Watch Out for These Misconceptions

Common Misconception

Torque remains constant regardless of loop orientation.

What to Teach Instead

Torque peaks at θ=90° due to sinθ factor, zero when aligned. Hands-on rotation demos let students measure deflections at angles, plot graphs, and self-correct via peer comparison to formula.

Common Misconception

Galvanometer directly measures voltage.

What to Teach Instead

It measures current; voltage needs series resistance. Circuit-building activities clarify by showing current division, helping students trace paths and calculate drops.

Common Misconception

Torque equals net force on loop.

What to Teach Instead

Uniform field gives zero net force but couple torque. Model setups with balanced forces but rotation reveal this distinction through observation and free-body sketches.

Active Learning Ideas

Demo Setup: Current Loop Torque

Provide soft straws, insulated wire, battery, and bar magnets. Students wind 10-20 turns on straw, connect circuit, place in field, and observe rotation by varying current or angle. Measure equilibrium angle with protractor and compare to sinθ predictions.

35 min·Small Groups

Model Build: Simple Galvanometer

Use thin aluminium strip as pointer, wind coil on frame, suspend with thread over magnet. Pass low DC current, note deflection. Adjust suspension tension and record θ vs I, plotting graph to verify linearity.

45 min·Pairs

Design Challenge: Instrument Conversion

Give galvanometer specs (G=30Ω, Ig=1mA). Pairs calculate shunt Rs for 5A ammeter and series R for 10V voltmeter. Sketch circuits, simulate with multimeter or breadboard if available, test predictions.

40 min·Pairs

Angle Variation Experiment

Fix loop area and current, rotate in field at 0°, 45°, 90°. Measure torque via deflection scale or spring balance. Groups tabulate sinθ vs torque, discuss equilibrium positions.

30 min·Small Groups

Real-World Connections

• Electrical engineers use the principles of torque on current loops to design electric motors, which are fundamental to countless machines from ceiling fans to electric vehicles.
• Instrument makers in scientific equipment manufacturing calibrate sensitive galvanometers and their conversions to ammeters and voltmeters for precise measurements in laboratory instruments and industrial control systems.
• Naval architects consider magnetic fields and their interactions when designing ship compasses and ensuring sensitive electronic equipment is shielded from interference.

Assessment Ideas

Quick Check

Present students with a diagram showing a current loop in a magnetic field at different angles (e.g., 0, 30, 60, 90 degrees). Ask them to calculate the torque in each case using τ = NIAB sinθ, assuming N=1, I=1A, A=0.1m², B=0.5T. Then, ask which orientation yields maximum torque.

Discussion Prompt

Pose the question: 'A galvanometer shows full-scale deflection for a current of 1 mA. How would you modify it to measure a current of 1 A? What about measuring a voltage of 10 V?' Facilitate a class discussion on the roles of shunt and series resistances.

Exit Ticket

On a small slip of paper, ask students to write down the formula for the torque on a current loop and briefly explain why a radial magnetic field is important for the working of a moving coil galvanometer.

Frequently Asked Questions

What is torque on a current loop in magnetic field?

Torque τ = N I A B sinθ acts to rotate the loop so its plane becomes perpendicular to B. For rectangular loop, forces on opposite sides form couple. Students compute for given values, predict stable positions. This scales with turns and area, key for devices like motors and galvanometers in CBSE curriculum.

How does moving coil galvanometer work?

Coil in radial field experiences torque τ = N I B A, balanced by kθ from suspension, so θ proportional to I. Pointer shows deflection on scale. Deadbeat design uses damping. Sensitivity improves with more turns, stronger B, lighter coil.

How to convert galvanometer to ammeter or voltmeter?

For ammeter, parallel shunt Rs = (Ig G)/(I - Ig) bypasses excess current. For voltmeter, series Rv = V/Ig - G limits current. Calculations ensure full scale deflection. Labs verify with known sources, building measurement skills.

How can active learning help with torque on current loop?

Building coils and observing torque with real magnets gives direct evidence of sinθ effect, far beyond diagrams. Group designs for conversions reinforce calculations through trial. Data logging and peer teaching solidify predictions, reduce abstraction, and boost retention in electromagnetism.