Q.A closely wound solenoid of 800 turns and area of cross section 2.5×10−4m2 carries a current of 3.0A. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?
Imagine you have a bar magnet — the kind you might have stuck on your refrigerator. If you bring two of them close, something interesting happens. Sometimes they snap together with a satisfying click. Other times, they push each other away, refusing to touch no matter how hard you try.
That's not random. Every magnet has two special regions, one at each end, where the magnetic force is strongest. These are its magnetic poles.
Note
The word "pole" comes from the Greek polos, meaning "pivot" or "axis" — the Earth itself has a North Pole and a South Pole, and it behaves like a giant magnet.
The Two Types of Poles
Every magnet has exactly two poles: a north pole and a south pole. You cannot have a magnet with only one pole — cut a bar magnet in half, and each half immediately becomes a complete magnet with its own north and south poles.
The rule of interaction is simple and memorable:
Unlike poles attract: north pulls south, south pulls north.
Like poles repel: north pushes north away; south pushes south away.
This is the fundamental behaviour. No exceptions.
The Precise Statement
Magnetic poles are the regions of a magnet where the external magnetic field is strongest. Every magnet has exactly two poles — a north pole and a south pole — that cannot be isolated. Like poles repel; unlike poles attract.
The key points to remember for exams:
Poles always come in pairs — there is no magnetic monopole (a single isolated pole) in nature, despite decades of searching.
The north pole is defined as the pole that points toward Earth's geographic north when the magnet is freely suspended.
The south pole points toward Earth's geographic south.
A Common Confusion (Watch Out)
Watch out
Earth's geographic North Pole is actually a magnetic south pole. Why? Because the north pole of a compass needle (which is a magnetic north pole) is attracted to it. And unlike poles attract. So the Earth's north pole behaves like a magnetic south pole. This often trips students up in exams.
Why This Matters
Magnetic poles are the starting point for understanding everything from simple compasses to electric motors, generators, and MRI machines. The idea that "opposites attract" in magnetism is the same principle that makes electric charges behave the way they do — but with one crucial difference: you can have a single positive or negative electric charge, but you can never have a single magnetic pole.
That asymmetry is one of the deepest facts about magnetism.
The behaviour of magnetic poles — always in pairs, with like poles repelling and unlike poles attracting — is covered in the NCERT Class 12 Physics chapter on magnetism and matter, a frequent source of short-answer CBSE board questions. Searches for "magnetic poles and Earth's magnetism class 12 physics" will find this north-south pole explanation, including the Earth's-north-pole-is-a-magnetic-south-pole detail, matches the NCERT textbook's own framing.
Why this formula?
Magnetic Poles: Why the Key Formulas Hold
Let's build this from first principles — understanding why a magnetic pole behaves the way it does, not just memorizing the result.
1. What Is a Magnetic Pole?
A magnetic pole is a conceptual point where the magnetic field appears to originate or terminate. In reality, magnetic poles always come in north-south pairs (no isolated monopoles exist in nature), but we treat them as idealized sources for calculations.
North pole: source of magnetic field lines (outward)
South pole: sink of magnetic field lines (inward)
2. The Key Formula: Force Between Two Magnetic Poles
The force between two magnetic poles of strengths m1 and m2, separated by distance r, is:
F=4πμ0⋅r2m1m2
Why this form?
This is a Coulomb's law analog — and that's not a coincidence. Here's the reasoning:
Experimental observation: Magnetic poles attract/repel with a force that:
Varies as 1/r2 (inverse square law)
Is proportional to the product of pole strengths
Depends on the medium (via μ0, the permeability of free space)
Mathematical analogy: The magnetic field B at distance r from a single pole m is:
B=4πμ0⋅r2m
This comes from Gauss's law for magnetism applied to a point source.
Force derivation: The force on pole m2 in the field of pole m1 is:
F=m2⋅B1=m2⋅(4πμ0⋅r2m1)
Hence:
F=4πμ0⋅r2m1m2
Key insight: The 1/r2 dependence is not arbitrary — it follows from the geometry of 3D space (flux spreads over a sphere of area 4πr2).
3. The Magnetic Field of a Bar Magnet (Two Poles)
For a bar magnet of length 2l with poles +m and −m, the field at a point on the axis at distance x from the center is:
B=4πμ0⋅(x2−l2)22ml
Why this form?
Superposition principle: The total field is the vector sum of fields from the north pole (+m) and south pole (−m).
Field from north pole at distance (x−l):
BN=4πμ0⋅(x−l)2m(away from north)
Field from south pole at distance (x+l):
BS=4πμ0⋅(x+l)2m(toward south)
Net field (both along same direction on axis):
B=BN−BS=4πμ0m[(x−l)21−(x+l)21]
Simplify using algebra:
(x−l)21−(x+l)21=(x2−l2)24xl
Therefore:
B=4πμ0⋅(x2−l2)24mxl
But for a bar magnet, the magnetic moment is M=m⋅(2l) (pole strength × separation). So 2ml=M, giving:
B=4πμ0⋅(x2−l2)22Mx
Key insight: The field is not simply 1/r2 because we have two poles — the net effect is a dipole field, which falls off as 1/r3 at large distances.
4. The Far-Field Approximation (Dipole Formula)
For x≫l (far from the magnet), x2−l2≈x2, so:
B≈4πμ0⋅x32M
Why 1/x3?
A single pole gives 1/r2
Two opposite poles separated by distance d give a dipole — the fields nearly cancel at large distances, leaving a weaker 1/r3 dependence
This is a universal property of dipoles (electric or magnetic)
5. Torque on a Magnetic Dipole in a Uniform Field
τ=MBsinθ
Why this form?
Force on each pole: In uniform field B, north pole feels F=mB along field, south pole feels F=mB opposite field.
Torque calculation: These equal and opposite forces form a couple:
Lever arm = 2lsinθ (perpendicular distance between forces)
Torque = force × lever arm = (mB)×(2lsinθ)
Using magnetic momentM=m⋅2l:
τ=MBsinθ
Key insight: The torque tries to align the magnet with the field — this is why a compass needle points north.
Summary Table: Why Each Formula Has Its Form
Formula
Key Reason
F∝1/r2
Flux spreads over sphere area 4πr2
F∝m1m2
Force is proportional to source strength (linear response)
B∝1/x3 (dipole)
Two opposite poles nearly cancel; residual is dipole field
τ=MBsinθ
Lever arm depends on sinθ in a couple
Remember: Every formula in magnetism is either a Coulomb analog (for poles) or a superposition of such analogs. The 1/r2 law is the foundation — everything else builds on it.
Concept: Magnetic Materials – Magnetization
A current-carrying solenoid behaves like a bar magnet because the magnetic field lines emerge from one end (north pole) and enter the other (south pole), exactly as in a permanent magnet. The sense is determined by the direction of current: using the right-hand rule, if current flows clockwise when viewed from one end, that end is the south pole; anticlockwise gives the north pole.
Reasoning
Magnetic moment of a solenoid is M=NIA, where N is number of turns, I is current, A is cross-sectional area.
The solenoid acts like a bar magnet with its north-south poles determined by current direction, and its magnetic moment is 0.6A⋅m2.
A current-carrying solenoid behaves like a bar magnet because its magnetic field lines emerge from one end (north pole) and enter the other (south pole). The magnetic moment is m=NIA=800×3.0×2.5×10−4=0.60A⋅m2.
The key insight is that a solenoid is simply a long coil of wire. When current flows through it, each turn produces a tiny circular magnetic field. Because the turns are closely wound, these fields add up coherently along the axis, creating a uniform field inside the solenoid that is very similar to the field inside a bar magnet.
Outside the solenoid, the field lines loop from one end to the other — exactly like the field of a bar magnet. One end behaves as a north pole (where field lines emerge) and the other as a south pole (where they re-enter). The sense (which end is north) is given by the right-hand rule: if you curl your fingers in the direction of the current, your thumb points toward the north pole.
The magnetic moment of a solenoid is the total magnetic dipole moment it produces. For a closely wound solenoid, this is simply the product of the number of turns, the current, and the cross-sectional area.
Identify the quantities
Number of turns: N=800
Current: I=3.0A
Cross-sectional area: A=2.5×10−4m2
Apply the formula for magnetic moment of a solenoid
For a single current loop, the magnetic moment is m=IA. For N identical turns carrying the same current, the total moment is the vector sum. Since the turns are closely wound and coaxial, their moments add directly:
m=NIA
Substitute the values
m=800×3.0×2.5×10−4
First multiply 800×3.0=2400
Then 2400×2.5×10−4=6000×10−4=0.60
State the result with units
The magnetic moment is 0.60A⋅m2.
Watch out
A common mistake is to forget that the area must be in m2 and current in amperes. Here 2.5×10−4m2 is already correct, but if area were given in cm2, you would need to convert (1cm2=10−4m2).
Tip
The direction of the magnetic moment is along the axis of the solenoid, pointing from the south pole to the north pole. So if you know the current direction, you can determine which end is north using the right-hand rule.
✓Final answer
The solenoid acts like a bar magnet with its north pole determined by the right-hand rule, and its magnetic moment is 0.60A⋅m2.
Method: Magnetic Moment of a Solenoid as an Equivalent Bar Magnet
Concept: A current-carrying solenoid behaves like a bar magnet because the magnetic field lines outside it run from one end (north pole) to the other (south pole), exactly like a bar magnet. The magnetic moment of the solenoid quantifies this behaviour.
Steps
Identify the formula
The magnetic moment (m) of a closely wound solenoid is given by:
m=NIA
where:
N = total number of turns
I = current in amperes
A = cross-sectional area in m2
List the given values
N=800
I=3.0A
A=2.5×10−4m2
Substitute into the formula
m=800×3.0×(2.5×10−4)
Calculate step-by-step
First: 800×3.0=2400
Then: 2400×2.5×10−4=6000×10−4=0.6
Write the final result
m=0.6A m2
Sense in which the solenoid acts like a bar magnet
The end from which the magnetic field lines emerge (using the right-hand grip rule: curl fingers along current direction, thumb points to north pole) behaves as the north pole.
The opposite end behaves as the south pole.
The magnetic moment vector points from the south pole to the north pole inside the solenoid (same direction as the axial field).
Thus, the solenoid is equivalent to a bar magnet of magnetic moment 0.6A m2 with its north-south axis along the solenoid's length.
Common Mistakes & How to Avoid Them
Mistake 1: Confusing Magnetic Moment with Magnetic Field
The error: Students often try to calculate the magnetic field B inside the solenoid instead of the magnetic moment m.
Why it happens: The formula B=μ0nI is drilled in, so students reach for it automatically.
How to avoid:
Magnetic momentm tells you how strong a magnet the solenoid behaves as — it's a dipole property.
Magnetic fieldB is the field produced inside the solenoid.
For a solenoid acting like a bar magnet, the relevant quantity is:
m=NIA
where N = total turns, I = current, A = cross-sectional area.
Correct calculation:
m=(800)(3.0)(2.5×10−4)=0.6A m2
Mistake 2: Forgetting the Direction (Sense) of the Magnetic Moment
The error: Students give only the magnitude and ignore the "sense" asked in the question.
Why it happens: The phrase "explain the sense" is overlooked — students think only numerical answer is needed.
How to avoid:
The sense means: which end behaves as North pole and which as South pole.
Use the right-hand thumb rule:
Curl fingers along the direction of current.
Thumb points to the North pole of the equivalent bar magnet.
State clearly:
The solenoid behaves like a bar magnet with its North pole at the end from which the current appears anticlockwise (when viewed along the axis).
Mistake 3: Using n (turns per unit length) Instead of N (total turns)
The error: Plugging n=800/length when length is not given.
Why it happens: Many problems give n, so students default to it.
How to avoid:
Read carefully: "800 turns" means total turnsN=800.
The formula m=NIA uses total turns, not turns per meter.
If length were given, you'd use n=N/L, but here it's not needed.
Mistake 4: Unit Errors in Area Conversion
The error: Writing 2.5×10−4m2 as 2.5cm2 or forgetting the 10−4.
Why it happens: Area is given in scientific notation — students misplace the decimal.
How to avoid:
Always write the unit explicitly: A=2.5×10−4m2.
Double-check: 1cm2=10−4m2, so this area is 2.5cm2 — but keep it in SI units for calculation.
Mistake 5: Not Explaining the "Bar Magnet" Analogy
The error: Giving only the formula and answer, skipping the conceptual explanation.
Why it happens: Students treat it as a plug-and-chug problem.
How to avoid:
Write a short paragraph:
A current-carrying solenoid produces a uniform magnetic field inside, similar to a bar magnet. The field lines emerge from one end (North) and enter the other (South). The magnetic moment points from South to North inside the solenoid, just like in a bar magnet.
Final Answer (Exam-Ready)
Magnetic moment:
m=NIA=800×3.0×2.5×10−4=0.6A m2
Sense:
The solenoid acts like a bar magnet with its North pole at the end where the current flows anticlockwise (viewed along the axis). The magnetic moment vector points from the South pole to the North pole inside the solenoid.