Explain magnetic moment.

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Q. Explain magnetic moment.

Bihar BsebBihar Board Intermediate 2022Subjective· 2mImportance★★★★★

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Concept understanding — Magnetic Moment of a Current Loop

Magnetic Moment of a Current Loop

Think of a tiny compass needle. It has a north pole and a south pole, and when you put it in a magnetic field, it feels a torque — a twist that tries to align it with the field. A current-carrying loop behaves exactly the same way. It's not a permanent magnet, but it acts like one: it has its own magnetic "strength" and a preferred direction, and an external field will try to rotate it.

That "magnetic strength" of the loop is called its magnetic moment. The bigger the current, the stronger the effect. The larger the area enclosed by the loop, the stronger the effect. And if you stack many loops together (N turns), each turn contributes, so the effect multiplies.

The Precise Definition

For a flat loop of wire carrying a steady current, the magnetic moment $\vec{m}$ is defined as:

\vec{m} = N I \vec{A}

Here:

$N$ is the number of turns of wire (if it's a single loop, $N=1$ ).
$I$ is the current flowing through the loop.
$\vec{A}$ is a vector whose magnitude equals the area enclosed by the loop, and whose direction is perpendicular to the plane of the loop.

The direction of $\vec{A}$ — and therefore of $\vec{m}$ — is given by the right-hand rule: curl the fingers of your right hand in the direction of the current; your thumb points along the magnetic moment.

Important

The magnetic moment is a vector quantity. Its magnitude is $m = NIA$ , and its direction is normal to the plane of the loop, following the right-hand rule.

Why This Makes Sense

A single moving charge produces a magnetic field. A current is a stream of moving charges. When those charges go around a loop, their individual magnetic fields add up. The net effect far away from the loop is identical to that of a tiny bar magnet placed at the centre of the loop, with its north pole pointing along $\vec{m}$ .

The torque this loop experiences in a uniform external magnetic field $\vec{B}$ is:

\vec{\tau} = \vec{m} \times \vec{B}

The magnitude of the torque is $mB\sin\theta$ , where $\theta$ is the angle between $\vec{m}$ and $\vec{B}$ . This is exactly the same formula as for a bar magnet. The loop tries to align its magnetic moment with the field — just like a compass needle.

Tip

For a square loop of side $L$ , area $A = L^2$ . For a circular loop of radius $r$ , area $A = \pi r^2$ . The formula $m = NIA$ works for any flat shape.

A Common Exam Point …

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Magnetic moment $M=m(2l)$ for a magnet and $M=NIA$ for a current loop — a vector, unit A·m².

The magnetic (dipole) moment measures the strength of a magnetic dipole and hence the torque it experiences in a magnetic field. It is a vector quantity directed from the south pole to the north pole (for a magnet) or along the area normal by the right-hand rule (for a loop).

For a bar magnet:

$M = m\times 2l,$

where $m$ is the pole strength and $2l$ the magnetic length.

For a current loop:

$M = N I A,$

where $N$ = number of turns, $I$ = current, $A$ = area of the loop.

…

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

Showing the 12 most recent of 14 on this concept.

CBSE 2026Set A1 markMCQ
$Q. A circular loop radius R carries a current I. Its magnetic dipole moment is (A) IR^2 (B) IR (C) 2π IR (D) πIR^2$
›Reveal solutionSolution

Magnetic dipole moment m = current × area = I·πR² for a circular loop of radius R.

The magnetic dipole moment of a plane current loop is

$m = N I A$ …

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CBSE 2026Set ANNUAL1 mark
$Q. Fill in the blank: If coil is viewed from one end and the current flows in clockwise direction, then this end is a ............... pole.$
›Reveal solutionSolution

By the clock rule for a current-carrying coil: clockwise current (as viewed) marks a South pole, anticlockwise marks a North pole.

For a current loop behaving as a magnet, use the right-hand rule (curl fingers along the current direction, thumb points to the North pole face). Equivalently, using the simple clock rule: if current appears to flow clockwise when v …

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CBSE 2025Set 55/5/11 markMCQ
$\dfrac{10}{\pi}$
›Reveal solutionSolution
The magnetic dipole moment of a current loop equals the product of current and loop area; for a circular loop with $I = \frac{10}{\pi}$ A and $r = 0.14$ m, we get $M = 0.196$ A m².

The magnetic dipole moment is a measure of how strongly a current loop behaves as a magnetic source. Just as an electric dipole has a dipole moment $p = qd$ , a current loop creates a magnetic field pattern identical to that of a bar magnet, characterized by its magnetic moment.

The key insight is that the magnetic dipole moment depends on two factors: how much current flows (the strength of the moving charges) and how large an area the current encloses (the spatial extent of the loop). The larger either quantity, the stronger the magnetic effect.
$M = I \cdot A$
where $M$ is the magnetic dipole moment, $I$ is the current, and $A$ is the area enclosed by the loop.

Now let's calculate step by step:

Identify the given quantities

Current: $I = \frac{10}{\pi}$ A

Radius: $r = 14$ cm $= 0.14$ m

Calculate the area of the circular loop

For a circle, $A = \pi r^2$ :

$A = \pi \times (0.14)^2 = \pi \times 0.0196 \text{ m}^2$

Compute the magnetic dipole moment …
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CBSE 2025Set ANNUAL1 markMCQ
$Q. Two wires of same length are shaped into a square and a circle. If they carry the same current, the ratio of the magnetic moments is$
(i) 2 : pi
(ii) pi : 2
(iii) pi : 4
(iv) 4 : pi
›Reveal solutionSolution

Magnetic moment m = IA; comparing areas for equal perimeter L gives square : circle = pi : 4.

For the square, side $= L/4$ , area $A_s = (L/4)^2 = L^2/16$ . For the circle, circumference $L = 2\pi r \Rightarrow r = L/2\pi$ , area $A_c = \pi r^2 = \pi \cdot \frac{L^2}{4\pi^2} = \frac{L^2}{4\pi}$ . Same current I, so $m = IA$ and …

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CBSE 2024Set 55/2/11 markMCQ
$4{\cdot}4$
›Reveal solutionSolution
The magnetic moment of a current loop is $M = NIA$ , where $N=1$ , $I=1.0\ \text{A}$ , and the area $A$ comes from the wire length $L = 4.4\ \text{m}$ forming the circumference. The radius is $r = L/(2\pi) \approx 0.700\ \text{m}$ , so $A = \pi r^2 \approx 1.54\ \text{m}^2$ , giving $M \approx 1.54\ \text{Am}^2$ . The correct option is (B).

Concept and intuition

The magnetic moment of a current-carrying loop is a measure of how strong a magnet the loop behaves like. For a single turn, it’s simply the product of the current and the area enclosed: $M = I A$ . The wire length here is the circumference of the loop — that’s the only link between the given length and the area. So the problem reduces to: given the circumference, find the radius, then the area, then multiply by current.

A common mistake is to forget that the wire length is the circumference, not the diameter or something else. Also, watch the decimal: $4.4$ m is exact, and the answer choices are given to two decimal places, so we need to compute carefully.

Step-by-step solution

Identify the loop geometry

The wire is bent into a single circular loop, so the number of turns $N = 1$ . The total length of the wire $L = 4.4\ \text{m}$ is exactly the circumference of the circle.

Find the radius from the circumference

Circumference $C = 2\pi r = L$ .

$r = \frac{L}{2\pi} = \frac{4.4}{2\pi} = \frac{2.2}{\pi}$
Using $\pi \approx 3.1416$ ,
$r \approx \frac{2.2}{3.1416} \approx 0.700\ \text{m}$
(You can keep it as $\frac{2.2}{\pi}$ for exactness until the final step.)

Compute the area of the loop Area of a circle: $A = \pi r^2$ .

$A = \pi \left( \frac{2.2}{\pi} \right)^2 = \pi \cdot \frac{4.84}{\pi^2} = \frac{4.84}{\pi}$
Numerically,

$A \approx \frac{4.84}{3.1416} \approx 1.540\ \text{m}^2$ …
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CBSE 2023Set 55/3/11 markMCQ
$Q. Two statements are given - one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (a), (b),$
(c) and
(d) below.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is also false. Assertion (A) : When the radius of a circular loop carrying a steady current is doubled, its magnetic moment becomes four times. Reason (R) : The magnetic moment of a circular loop carrying a steady current is proportional to the area of the loop.
›Reveal solutionSolution
The magnetic moment of a current loop is $M = I \cdot A$ , so doubling the radius quadruples the area and thus the magnetic moment. Both Assertion and Reason are true, and the Reason correctly explains the Assertion — answer is (a).

The heart of this question is the magnetic moment of a current-carrying loop. Magnetic moment is the fundamental quantity that determines how a current loop behaves in an external magnetic field — it experiences a torque trying to align it with the field, just like a compass needle.

For any planar loop carrying a steady current $I$ , the magnetic moment $\vec{M}$ is defined as:
$\vec{M} = I \cdot \vec{A}$
where $\vec{A}$ is the area vector of the loop (magnitude = area, direction = perpendicular to the plane, given by the right-hand rule). This is a direct, proportional relationship — double the current, double the moment; double the area, double the moment.

Now let's apply this to the specific statements.

Assertion (A): A circular loop of radius $r$ has area $A = \pi r^2$ . Its magnetic moment is $M = I \cdot \pi r^2$ . If the radius is doubled to $2r$ , the new area becomes $A' = \pi (2r)^2 = 4\pi r^2 = 4A$ . Since current $I$ is unchanged (steady current), the new magnetic moment is $M' = I \cdot 4\pi r^2 = 4M$ . So the magnetic moment indeed becomes four times. Assertion (A) is true.

Reason (R): The statement says magnetic moment is proportional to the area of the loop. From $M = I A$ , with $I$ constant, $M \propto A$ . This is exactly correct. Reason (R) is true. …
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CBSE 2023Set F1 markMCQ
$Q. The radius of a circular current loop is made double and the current is made half. The magnetic moment of the loop will become (A) Halved (B) Doubled (C) Four times large (D) None of these$
›Reveal solutionSolution

$M = I\pi r^2$ ; area ×4 and current ×½ ⇒ moment ×2.

The magnetic moment of a single circular current loop is

$M = I A = I\,\pi r^2.$

New radius $r' = 2r \Rightarrow$ area becomes $\pi (2r)^2 = 4\pi r^2$ (×4).

New current $I' = I/2$ (×½).

…

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CBSE 2023Set ANNUAL1 mark
$Q. Current loop behaves as a ________. (Magnetic dipole/Electric dipole)$
›Reveal solutionSolution

A current-carrying loop produces a magnetic field pattern identical to that of a bar magnet (a magnetic dipole), with a magnetic moment $m = NIA$ .

A planar loop of area A carrying current I has a magnetic moment $\vec{m} = I\vec{A}$ (or $NIA$ for N turns), directed normal to the plane of the loop as given by the right-hand rule. Far from the loop, its magnetic field falls off with distance and is oriented exactly like the field of a short bar magnet with a north and south pole. This loop–magnet equivalence is why a c …

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CBSE 2023Set ANNUAL1 markMCQ
$n$
(a) $n^2IA$
(b) $nIA^2$
(c) $nIA$
(d) $nI^2A$
›Reveal solutionSolution

The magnetic (dipole) moment of a current loop is the product of the number of turns, the current and the area.

Solution:

For a plane current loop of $n$ turns, each carrying current $I$ and enclosing area $A$ , each turn behaves as a magnetic dipole of moment $IA$ (current × area), directed normal to the plane of the loop (right-hand rule). Since …

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CBSE 2022Set I1 markMCQ
$Q. Electromagnetic moment of current carrying coil is (A) NI A (B) N A/I (C) N/(I A) (D) I A/N$
›Reveal solutionSolution

The magnetic (dipole) moment of a coil is m = N I A.

For a plane coil of N turns, each carrying current I and enclosing area A, the magnetic dipole moment is

$m = N I A$

…

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CBSE 2022Set I1 markMCQ
$Q. Electromagnetic moment of current carrying coil is (A) m = N A/I (B) m = A/(NI) (C) m = NI A (D) m = I A/N$
›Reveal solutionSolution

Magnetic moment of a coil $m = NIA$ .

A single planar loop carrying current $I$ and enclosing area $A$ has a magnetic dipole moment $m = IA$ , directed normal to the plane of the loop (right-hand rule).

…

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CBSE 2020Set 55/1/11 markMCQ
$Q. The magnetic dipole moment of a current carrying coil does not depend upon (A) number of turns of the coil. (B) cross-sectional area of the coil. (C) current flowing in the coil. (D) material of the turns of the coil.$
›Reveal solutionSolution
The magnetic dipole moment $\mu = NIA$ depends only on the current, number of turns, and loop area — not on what the wire is made of. The answer is (D).

The magnetic dipole moment is a measure of the strength of a current loop as a magnetic source. To understand what it depends on, we need to see where it comes from.

When a steady current flows through a closed loop, it creates a magnetic field pattern identical to that of a tiny bar magnet. The strength of this "equivalent magnet" is quantified by the magnetic dipole moment. For a single circular loop carrying current $I$ and enclosing area $A$ , the dipole moment is:
$\mu = IA$
This is a vector quantity, with direction given by the right-hand rule (curl your fingers along the current, thumb points along $\mu$ ).

Now let's examine each factor systematically:

Number of turns ( $N$ ): If you stack $N$ identical loops carrying the same current, each contributes $IA$ to the total moment. They add up because the magnetic fields from each turn reinforce one another. The total moment becomes:

$\mu = NIA$
So the dipole moment is directly proportional to the number of turns.

Cross-sectional area ( $A$ ): A larger loop encloses more area, which means more magnetic flux threads through it and a stronger field is produced at distant points. The moment scales linearly with area — double the area, double the moment.

Current ( $I$ ): The magnetic field strength is directly proportional to the current flowing. More current means more moving charge per unit time, hence a stronger magnetic effect. The moment is directly proportional to $I$ .

Material of the wire: Here's the key insight. The magnetic dipole moment depends only on the current (charge flow rate), not on how that current is achieved. Whether the wire is copper, aluminum, silver, or any other conductor, as long as the same current $I$ flows through the same geometry, the magnetic moment is identical. …
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Q.Explain magnetic moment.

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