C
CraftExam
medium difficulty11 min

Magnetic Dipole Moment of a Current Loop and Bar Magnet

Magnetic dipole moment is a vector quantity that measures the strength and orientation of a magnetic dipole. For a plane current loop, its magnitude is m = NIA.

In one line: Current loop strength is turns times current times area: NIA.

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Understand it

  • A current-carrying loop behaves like a magnetic dipole.
  • Its magnetic dipole moment depends on the number of turns N, current I, and area A of the loop.
  • The direction of the dipole moment is perpendicular to the plane of the loop, given by the right-hand thumb rule.
  • A bar magnet can also be treated as a magnetic dipole, with its dipole moment directed from south pole to north pole inside the magnet.

Example

A circular coil with 50 turns, current 0.20 A, and area 4.0 × 10−3 m2 has magnetic dipole moment m = NIA = 50 × 0.20 × 4.0 × 10−3 = 4.0 × 10−2 A m2.

Formula and rule

Formula: m = NIA.

Here m is magnetic dipole moment in A m2, N is number of turns with no unit, I is current in ampere, and A is area in m2.

Torque in a uniform magnetic field is tau = m × B, with magnitude tau = mB sin θ, where B is magnetic field in tesla and θ is the angle between m and B.

Use these formulas for current loops, coils, and equivalent dipole treatment of magnets in a uniform magnetic field.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A coil of 100 turns has area 2.5 × 10−3 m2 and carries current 0.40 A.

  1. 1Find its magnetic dipole moment and maximum torque in a 0.20 T field.
  2. 2Calculation: m = NIA = 100 × 0.40 × 2.5 × 10−3 = 0.10 A m2.
  3. 3Maximum torque occurs when sin θ = 1, so taumax = mB = 0.10 × 0.20 = 0.020 N m.
  4. 4Interpretation: the coil experiences maximum turning effect when its dipole moment is perpendicular to the field.

Method you can reuse

For numerical questions: note N, I, A, B, and θ; calculate m = NIA; if torque is asked, substitute in tau = mB sin θ; write SI units at each stage; interpret maximum or zero torque from the value of θ.

Visual tip

A useful diagram shows a current loop, direction of current, area vector perpendicular to the loop, and magnetic dipole moment along the area vector. For torque, show m making angle θ with uniform B.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What happens to the magnetic dipole moment of a coil if the number of turns is doubled while current and area remain unchanged?

Think first, then show answer
The magnetic dipole moment doubles because m = NIA. If I and A stay the same, m is directly proportional to the number of turns N.

Common wrong answer

Using tau = mB for every angle is wrong. tau = mB only for θ = 90 degrees; the general expression is tau = mB sin θ.

Don't mix this up

A frequent mistake is using radius instead of area in m = NIA, or forgetting to multiply by the number of turns N.

Exam tip

Always write the unit A m2 for magnetic dipole moment. For torque questions, use the vector relation tau = m × B and the magnitude tau = mB sin θ.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions usually ask for the formula and unit of magnetic dipole moment, calculation of m for a coil, or torque on a magnetic dipole placed at an angle in a uniform magnetic field.
  1. 1

    Enough for 1 mark

    Magnetic dipole moment is a vector quantity that measures the strength and orientation of a magnetic dipole. For a plane current loop, its magnitude is m = NIA.

  2. 2

    Add for 2 marks

    Example: A circular coil with 50 turns, current 0.20 A, and area 4.0 × 10−3 m2 has magnetic dipole moment m = NIA = 50 × 0.20 × 4.0 × 10−3 = 4.0 × 10−2 A m2.

  3. 3

    Add for 3 marks

    A current-carrying loop behaves like a magnetic dipole.

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