Physics Class 12 Part I…
🏠 Home Log in
TOPIC 16 OF 38

Force Between Currents Torque

🎓 Class 12 Physics CBSE Theory Ch 4 – Moving Charges and Magnetism ⏱ ~14 min
🌐 Language:

This MCQ module is based on: Force Between Currents Torque

This assessment will be based on: Force Between Currents Torque

Upload images, PDFs, or Word documents to include their content in assessment generation.

Force Between Currents Torque

4.9 Force on a Current-Carrying Conductor in a Magnetic Field

If a wire of length L carries a current I in an external magnetic field \(\vec B\), the force on the wire is the sum of forces on all moving carriers inside it. The result is delightfully simple:

\[\vec F = I\,\vec L \times \vec B\]

where \(\vec L\) points along the direction of current flow and has magnitude L. The magnitude is \(F = BIL\sin\theta\). Direction: by the right-hand rule applied to \(\vec L \times \vec B\).

4.10 Force Between Two Parallel Currents - Definition of the Ampere

Place two long, parallel straight wires a distance d apart, carrying currents \(I_1\) and \(I_2\). Wire 1 produces a field at the location of wire 2:

\(B_1 = \dfrac{\mu_0 I_1}{2\pi d}\)

Wire 2 (carrying \(I_2\), length L) experiences a force \(F = I_2 L B_1\), so the force per unit length on wire 2 is:

\[\dfrac{F}{L} = \dfrac{\mu_0\, I_1\, I_2}{2\pi d}\]

Direction (apply the right-hand rule):

  • Currents in the same direction: the wires attract each other.
  • Currents in opposite directions: the wires repel.
Parallel currents (attract) I1 I2 F (attract) Antiparallel currents (repel) I1 I2 F (repel)
Fig 4.10 Two long parallel wires experience a mutual force per unit length F/L = mu0 I1 I2 / (2 pi d).
Definition of the ampere (SI base unit): One ampere is the constant current which, if maintained in two straight parallel conductors of infinite length and negligible cross-section placed one metre apart in vacuum, produces between them a force of exactly \(2\times10^{-7}\) newton per metre of length.

Numerically: with \(I_1 = I_2 = 1\) A, d = 1 m, F/L = (4 pi x 10-7)(1)(1) / (2 pi x 1) = 2 x 10-7 N/m.

Worked Example 4.7 - Power-line wires

Example 4.7 L3 Apply

Two long parallel wires 50 cm apart carry currents 30 A and 25 A in the same direction. Find the force per metre.

F/L = mu0 I1 I2 / (2 pi d) = (4 pi x 10-7 x 30 x 25) / (2 pi x 0.50)

= (2 x 10-7 x 30 x 25) / 0.50 = 3.0 x 10-4 N/m, attractive.

4.11 Torque on a Current Loop in a Uniform Magnetic Field

Place a rectangular loop of length a, breadth b carrying current I in a uniform field \(\vec B\). The forces on the two sides of length b cancel each other (and lie along the axis), but the forces on the two sides of length a form a couple that tries to rotate the loop about its central axis.

B I F (out) F (in) m Loop area A = a x b, n carriers, current I
Fig 4.11 The two sides of length a in a uniform B form a couple; loop has magnetic moment m = NI A perpendicular to its plane.

If the plane of the loop makes angle theta with B (so the normal n-hat makes angle (90 - theta) with B...) - more cleanly, define the angle between magnetic moment m and B as theta. The torque magnitude is:

\[\tau = NIAB\sin\theta\]

and as a vector,

\[\vec\tau = \vec m \times \vec B,\qquad \vec m = NI\vec A\]

Here \(\vec m = NIA\,\hat n\) is the magnetic dipole moment of the loop. Direction of n-hat: curl the right-hand fingers in the direction of current flow; the thumb points along n-hat (and m).

Equilibria:
  • Stable equilibrium: m parallel to B (theta = 0). Torque zero, restoring torque on small disturbance.
  • Unstable equilibrium: m antiparallel to B (theta = 180°).
  • Maximum torque: theta = 90° (loop's plane parallel to B).

4.11.1 Potential energy of a magnetic dipole

By analogy with electric dipoles, the work done in rotating m through a small angle d theta is dW = tau d theta, hence

\(U = -\vec m \cdot \vec B = -mB\cos\theta\)

U is minimum (-mB) when m parallel to B (stable), maximum (+mB) when antiparallel.

4.11.2 The current loop as a magnetic dipole

Far from the loop, the magnetic field has the same form as that of an electric dipole, with the magnetic moment m playing the role of the electric dipole moment p. On the axis, far away (x >> R):

\(B_{axial} = \dfrac{\mu_0}{4\pi}\,\dfrac{2m}{x^3}\)
PropertyElectric DipoleMagnetic Dipole (loop)
Momentp = q d (C m)m = N I A (A m²)
Field on axis (r >> size)2 k p / r³(mu0/4 pi)(2m/r³)
Torquep x Em x B
Potential energy-p . E-m . B

Worked Example 4.8 - Torque on a coil

Example 4.8 L3 Apply

A 50-turn rectangular coil of size 4 cm x 6 cm carries 1.5 A in a uniform 0.20 T field. Find the maximum torque.

A = 0.04 x 0.06 = 0.0024 m².

m = N I A = 50 x 1.5 x 0.0024 = 0.18 A m².

tau_max = m B = 0.18 x 0.20 = 0.036 N m (at theta = 90°).

Worked Example 4.9 - Magnetic moment of a revolving electron

Example 4.9 L4 Analyse

An electron in a hydrogen atom revolves at frequency f = 6.6 x 1015 Hz in a circular orbit of radius r = 5.3 x 10-11 m. Find its magnetic moment.

Equivalent current: I = e f = (1.6 x 10-19)(6.6 x 1015) = 1.06 x 10-3 A.

Area of orbit: A = pi r² = pi(5.3 x 10-11)² = 8.83 x 10-21 m².

m = I A = (1.06 x 10-3)(8.83 x 10-21) = 9.36 x 10-24 A m² - one Bohr magneton.

Interactive: Torque on a Current Loop L4 Analyse

Vary the angle between the magnetic moment m and B, and see the torque change as tau = m B sin theta.

B-axis m
m = 0.12 A m^2, tau = 0.060 N m
Activity 4.3 - Two Parallel Foil Strips L3 Apply

Hang two thin aluminium foil strips a few centimetres apart from a common support so they hang vertically. Connect them in series with a battery and switch (with a current-limiting resistor) so the same current flows through both, but in opposite directions.

Predict: when you close the switch, do the strips move apart or come together?

The strips fly apart. Antiparallel currents repel - the same physics that limits how closely you can pack opposing-direction conductors in a power transformer.

Reverse the connection so currents are parallel and the strips will swing together (sometimes briefly touching). This visible mechanical effect is the basis for the SI definition of the ampere.

Competency-Based Questions L3-L5

A laboratory current balance has two horizontal coils. The lower coil is fixed; the upper coil is suspended from a sensitive balance. When the same current flows through both coils in the same direction, the upper coil is pulled downward; when reversed, it is pushed up.

Q1. Two long parallel wires 1 m apart carrying 1 A in the same direction experience what force per metre?

  • (a) 2 x 10-7 N/m, repulsive
  • (b) 2 x 10-7 N/m, attractive
  • (c) 4 pi x 10-7 N/m, attractive
  • (d) 0
(b). F/L = mu0 I1 I2 / (2 pi d) = 2 x 10-7 N/m, attractive (parallel currents).

Q2. (Short answer) Why is the torque on a current loop in a uniform field zero when m is parallel to B but maximum when m is perpendicular?

tau = m B sin theta. sin 0 = 0 - no rotational tendency when m aligned with B. sin 90° = 1 - the lever arm is maximum when m is perpendicular to B, giving maximum torque.

Q3. (Numerical) A 100-turn coil of area 10 cm² carries 0.5 A in a 0.1 T field. Maximum torque?

m = N I A = 100 x 0.5 x 10 x 10-4 = 0.005 A m². tau_max = m B = 0.005 x 0.1 = 5 x 10-4 N m.

Q4. (Fill in the blank) The potential energy of a magnetic dipole in a field is U = ___.

U = - m . B = - m B cos theta. Minimum (-mB) when aligned with B.

Q5. (HOT) A circular loop of wire is placed in a non-uniform magnetic field. Show that, in addition to a possible torque, there is a net translational force on the loop, and indicate its direction.

In a uniform B the forces on opposite sides cancel - net force = 0 (only torque). In a non-uniform B, the side where B is stronger feels a larger force than the side where B is weaker. The net force is F = grad(m . B). For m parallel to B, the loop is pulled toward stronger field (paramagnetic-like behaviour); for m antiparallel, repelled (diamagnetic-like). This is the basis of the Stern-Gerlach experiment.

Assertion-Reason Questions L4 Analyse

(a) Both A and R true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.

A: Two parallel wires carrying currents in the same direction attract each other.

R: The magnetic field of one wire creates a force on the moving charges of the other (F = I L x B), and the geometry forces it inward.

(a). Wire 1 produces B at wire 2 directed (say) into the page; the force F = I2 L x B on wire 2 then points toward wire 1.

A: The net force on a current loop in a uniform magnetic field is zero.

R: Each segment of the loop feels a force that cancels with the segment diametrically opposite.

(a). By symmetry, in a uniform field, opposite sides give equal-and-opposite forces; net F = 0 but a torque can still exist.

A: A current loop behaves like a magnet.

R: A current loop possesses a magnetic moment m = NIA and produces a dipole-like field at large distances.

(a). The far field of a current loop is identical (up to constants) to that of a bar magnet of the same dipole moment - this is Ampere's hypothesis on the origin of magnetism.

Frequently Asked Questions - Force Between Currents Torque

What is the main concept covered in Force Between Currents Torque?
In NCERT Class 12 Physics Chapter 4 (Moving Charges and Magnetism), "Force Between Currents Torque" covers the core principles and equations students need for board exam success. The MyAiSchool lesson explains the topic with definitions, derivations, worked examples, and interactive simulations. Key formulas and dimensional analysis are included to build conceptual depth and problem-solving skills aligned with the CBSE 2025-26 syllabus.
How is Force Between Currents Torque useful in real-life applications?
Real-life applications of "Force Between Currents Torque" from NCERT Class 12 Physics Chapter 4 include electronics, communication systems, medical imaging, solar energy, semiconductor devices, and modern technology. The MyAiSchool lesson links every concept to a tangible example so students see physics as a problem-solving framework for the physical world, not as abstract formulas.
What are the key formulas in Force Between Currents Torque?
Key formulas in "Force Between Currents Torque" (NCERT Class 12 Physics Chapter 4 Moving Charges and Magnetism) are derived step-by-step in the MyAiSchool lesson. Students should memorize the final formula AND understand its derivation for full board marks. Each formula is listed with its dimensional formula, SI unit, applicability range, and common pitfalls. The Summary section at the end of each part includes a quick-reference formula card.
How does this part connect to other parts of Chapter 4?
NCERT Class 12 Physics Chapter 4 (Moving Charges and Magnetism) is structured so each part builds on the previous one. "Force Between Currents Torque" connects directly to neighbouring parts via shared definitions, units, and methodology. The MyAiSchool lesson cross-references related concepts with internal links so students can navigate the whole chapter as one connected story rather than disconnected fragments.
What types of CBSE board questions come from Force Between Currents Torque?
CBSE board questions from "Force Between Currents Torque" typically include: (1) 1-mark MCQs on definitions and formulas, (2) 2-mark short-answer derivations or applications, (3) 3-mark numerical problems with units, (4) 5-mark long-answer derivations followed by application. The MyAiSchool lesson tags each Competency-Based Question (CBQ) with Bloom level (L1-L6) so students know how to study for each weight.
How can students use the interactive simulation effectively?
The interactive simulation in the "Force Between Currents Torque" lesson allows students to adjust input parameters (sliders or selectors) and see physical quantities update in real time. To use it effectively: (1) try extreme values to understand limiting cases, (2) compare with the analytical formula, (3) check unit consistency, (4) test special configurations from worked examples. The simulation reinforces conceptual intuition that pure formula manipulation cannot.
AI Tutor
Physics Class 12 Part I – NCERT (2025-26)
Ready
Hi! 👋 I'm Gaura, your AI Tutor for Force Between Currents Torque. Take your time studying the lesson — whenever you have a doubt, just ask me! I'm here to help.

📝 Practice this topic — Mock Exams

🎯 Practise Physics

Sit a full paper on what you have been studying, marked question by question.

Board exam sample papers

All papers for this subject →

Mock exams

All mock exams for this subject →

🎁 Join our community and get free AI credits!
WhatsApp