Why Magnetic Field Lines Form Closed Loops in HSC Physics

A bar magnet diagram often shows magnetic field lines leaving its north pole and entering its south pole. If the drawing stops there, it looks as though the magnetic field starts at N and disappears at S.

It doesn’t.

For a finite bar magnet, every magnetic field line continues through the magnet itself, travelling from south to north. The line then emerges from the north pole and travels through the surrounding space back towards the south pole. The result is a continuous, closed loop.

The reason is fundamental: ordinary magnets do not have isolated north or south magnetic poles. There are no magnetic sources or sinks where a magnetic field line can begin or end.

Before going further, predict something. If you place a small compass inside a solenoid, will its north end point in the same direction as a compass placed just outside the coil?

No. Inside the solenoid, the magnetic field points from S to N. Outside, it returns from N to S. These opposite directions are exactly what allow the field lines to form closed loops.

01Why magnetic field lines cannot simply stop at a pole

Think about what a magnetic field line actually represents.

It is an imaginary line used to describe the magnetic field, written as \(\vec B\). At any point, the direction of the line’s tangent tells you the direction of the magnetic field.

A small compass provides a practical way to determine this direction. Its north-seeking end aligns with the magnetic field.

For a conventional bar magnet, this gives us two directions:

• Outside the magnet: magnetic field lines travel from north to south.
• Inside the magnet: magnetic field lines travel from south to north.

The second direction is easy to overlook because diagrams often concentrate on the space surrounding the magnet.

However, the field doesn’t suddenly change its nature when it enters the magnet. It continues through the material.

Why don’t magnets have separate north and south poles?

Imagine breaking a bar magnet into two smaller pieces.

You might predict that the left piece would contain only the original north pole, while the right piece would contain only the original south pole.

That doesn’t happen.

Each smaller piece becomes a magnet with its own north and south poles. Breaking the magnet doesn’t produce an isolated magnetic pole.

This behaviour is consistent with the fact that isolated magnetic monopoles have never been observed.

A magnetic monopole would be an individual north or south magnetic charge. If one existed, magnetic field lines could begin or end at that charge, in much the same way that electric field lines begin on positive charges and end on negative charges.

But ordinary magnetic fields don’t behave this way.

Instead, magnetic field lines have no magnetic starting or finishing points. For the familiar finite magnets studied in HSC Physics, this produces closed loops.

This is the central difference between the usual electric and magnetic field-line models:

The important distinction is not simply that the diagrams look different. It comes from the different physical properties of electric and magnetic sources.

For a more detailed treatment of drawing and interpreting permanent-magnet patterns, see Magnetic Field Lines Around Permanent Magnets: HSC Physics.

02How experiments revealed the shape of magnetic fields

The idea that magnetic field lines form loops is easier to understand when you follow how scientists investigated magnetic fields.

The key was learning to use a compass to map the direction of an otherwise invisible field.

Oersted’s experiment: electricity produces magnetism

Before 1820, electricity and magnetism were commonly treated as separate physical phenomena.

Scientists knew that magnets could deflect compass needles, but the connection between electric current and magnetism was not yet established.

Danish physicist Hans Christian Oersted investigated this relationship using a relatively simple arrangement.

His apparatus consisted of:

• A battery supplying electrical energy.
• A conducting wire connected to the battery.
• A compass positioned close to the wire, with its needle approximately parallel to the wire.

The wire was positioned above the compass. When the circuit was completed, current flowed through the wire.

What should happen if the current has no magnetic effect?

The compass should remain pointing in its original direction.

Instead, the compass needle deflected.

Oersted then reversed the current. The compass deflected in the opposite direction.

This observation established two important ideas:

1. An electric current produces a magnetic field around the conductor.
2. Reversing the current reverses the direction of the magnetic field.

Oersted published his findings in July 1820. His discovery helped establish the connection between electricity and magnetism and prompted further investigations by scientists including André-Marie Ampère and Michael Faraday. American Physical Society

However, there was a limitation.

A single compass only tells us the magnetic field direction at one location. It cannot reveal the complete shape of the field.

To understand that shape, we need to map the field at many different positions.

Mapping the field around a current-carrying wire

Consider a straight wire passing vertically through a horizontal sheet of cardboard.

Connect the wire to a DC power supply so that conventional current flows upwards, towards an observer looking down at the cardboard.

Now place a small compass at different positions around the wire.

At each position:

1. Allow the compass needle to align with the magnetic field.
2. Mark the direction in which its north end points.
3. Move the compass to another position and repeat.
4. Join the recorded directions smoothly.

The resulting pattern is a series of concentric circles around the wire.

Notice something important.

The magnetic field doesn’t point directly away from the wire or towards it. It points tangentially around the wire.

The circular field lines are themselves closed loops.

If the current is reversed, the circular field lines remain circular, but their direction reverses.

This experiment provides a particularly useful demonstration of why magnetic field lines can form closed paths even when there isn’t a permanent magnet involved.

The source of the field is different, but the continuous nature of the magnetic field remains.

There is one experimental limitation worth remembering: an actual straight wire is part of a complete electrical circuit. Its return conductor also produces a magnetic field. The simple concentric-circle model describes a long, straight section where the effects of the return conductor can be neglected.

The solenoid: seeing the return path

A solenoid makes the closed-loop pattern even easier to understand.

A solenoid is a long coil of insulated conducting wire. When conventional current passes through its windings, it produces a magnetic field resembling that of a bar magnet.

Imagine a solenoid positioned horizontally, with its left end acting as a north pole and its right end acting as a south pole.

Place a small compass inside the hollow centre of the coil. Then move another compass to a position above the coil.

What should the two compasses show?

Inside the solenoid, the magnetic field points from S to N, so the north end of the compass points towards the left.

Outside the solenoid, the field returns from N to S, so the north end of the compass points towards the right.

The directions are opposite.

The observations can be summarised:

The solenoid therefore provides an accessible model of the same behaviour seen in a permanent magnet.

Its internal field is relatively strong and approximately uniform near the centre. Its external field is weaker, but it still forms part of the continuous magnetic field.

This is why the field lines don’t simply disappear when they reach the south end.

They return through the solenoid.

03The right-hand grip rule: finding the field direction

The experiments above reveal that electric currents can produce magnetic fields with circular or loop-like patterns.

But how do you determine which direction those fields point?

For a straight current-carrying wire, use the right-hand grip rule.

The rule is simple:

1. Point your right thumb in the direction of conventional current.
2. Curl your fingers naturally around the wire.
3. Your curled fingers show the direction of the magnetic field.

Throughout this explanation, current means conventional current: the direction in which positive charge would flow through the external circuit.

Electron flow in a metal is opposite to conventional current. Don’t accidentally use the electron direction when applying the right-hand grip rule.

If you need to revise that distinction, see Electron Flow vs Conventional Current in HSC Magnetic Questions.

Understanding the dot and cross notation

HSC Physics questions frequently show wires using dots and crosses.

These symbols represent a current flowing perpendicular to the page.

The direction changes because reversing the current reverses the magnetic field.

The shape doesn’t change.

This is an important distinction when interpreting diagrams: the current direction determines the magnetic field direction, but it does not directly tell you the direction of a magnetic force on another object.

04Magnetic field direction is not magnetic force direction

This is one of the most important distinctions in magnetic-field questions.

The right-hand grip rule tells you the direction of the magnetic field produced by a current.

It does not tell you the direction of the force experienced by a current-carrying wire placed in an external magnetic field.

These are different physical questions and require different direction rules.

Consider a wire carrying conventional current through a uniform external magnetic field.

The magnetic force on the wire has magnitude

\[
F=BIL\sin\theta
\]

where:

• \(F\) is the magnetic force in newtons (N).
• \(B\) is the external magnetic field strength in tesla (T).
• \(I\) is the conventional current in amperes (A).
• \(L\) is the length of conductor within the magnetic field in metres (m).
• \(\theta\) is the angle between the current direction and the external magnetic field.

The force acts perpendicular to both the current and the external magnetic field.

For its direction, use Fleming’s left-hand rule.

Why does this distinction matter?

Imagine an electron moving parallel to a magnetic field line. The electron experiences no magnetic force because its velocity is parallel to the field.

The magnetic field still exists.

This shows why magnetic field lines should not be interpreted as paths that particles follow or as directions in which magnetic forces must act.

A field line represents the direction of \(\vec B\), not the direction of every magnetic force.

05Worked examples

06When do magnetic field lines appear not to form loops?

You might occasionally see a magnetic field diagram containing straight, parallel lines that appear to extend indefinitely.

Does this contradict the closed-loop principle?

No. It usually means the diagram is showing an idealised region of a much larger magnetic field.

Consider a uniform magnetic field between two large magnet poles.

In the small region being studied, the field lines can be represented as straight, parallel lines with equal spacing. Their return paths are outside the region shown.

Similarly, an ideal infinitely long solenoid is modelled as having a uniform internal field and zero external field. A real, finite solenoid has fringe fields that return outside the coil.

There is an important distinction here:

• A magnetic field line cannot begin or end at an ordinary magnetic pole.
• A diagram can show only part of a field line.
• An idealised field can contain lines that extend indefinitely rather than forming visible loops within the model.

The closed-loop principle is about the absence of magnetic sources and sinks, not about forcing every diagram into a circular shape.

07Questions and solutions

Question 1

A bar magnet is positioned horizontally, with its north pole on the left and south pole on the right.

Describe the direction of the magnetic field:

(a) Outside the magnet.

(b) Inside the magnet.

Explain why the field lines form closed loops.

Solution 1

The magnetic field travels from N to S outside the magnet and from S to N inside the magnet. These opposite directions produce continuous closed loops.

(a) Outside the magnet

Magnetic field lines emerge from the north pole and curve around towards the south pole.

Their direction is:

\[
\text{N}\rightarrow\text{S}
\]

(b) Inside the magnet

The magnetic field continues through the magnet from the south pole towards the north pole.

Its direction is:

\[
\text{S}\rightarrow\text{N}
\]

The field does not terminate when it enters the south pole.

Explanation

Ordinary magnets do not contain isolated north or south magnetic poles. Consequently, magnetic field lines have no starting or finishing points.

The external and internal sections form one continuous path.

A common mistake is to draw arrows from N to S outside the magnet and then stop them at S. This only shows part of the magnetic field.

Question 2

A bar magnet has its north pole at the left end and its south pole at the right end.

The magnet is cut across its centre into two equal pieces. Neither piece is rotated, and the pieces are separated by a small gap.

(a) Identify the poles at all four ends of the two smaller magnets.

(b) Explain why this observation supports the closed-loop model of magnetic field lines.

(c) Describe the direction of the magnetic field inside each smaller magnet.

Solution 2

Each smaller piece becomes a complete magnet with its own north and south poles. Cutting the original magnet does not produce an isolated magnetic pole.

(a) Identify the four poles.

The original magnet has N on the left and S on the right.

After cutting:

• Left piece: original N at its far-left end and a new S at its cut face.
• Right piece: a new N at its cut face and original S at its far-right end.

The resulting arrangement is:

\[
\mathrm{N\quad S}\qquad
\mathrm{N\quad S}
\]

The two newly created faces have opposite magnetic polarities.

(b) Explain the observation.

The experiment demonstrates that the magnetic poles of an ordinary magnet cannot be separated simply by cutting the magnet into smaller pieces.

Each resulting piece still has both poles.

This is consistent with magnetic field lines forming continuous loops rather than beginning at an isolated north pole and terminating at an isolated south pole.

Strictly, cutting a magnet is not a mathematical proof that magnetic monopoles cannot exist. It demonstrates the behaviour of ordinary permanent magnets.

(c) Describe the internal field directions.

Inside each smaller magnet, the magnetic field travels from its south pole towards its north pole.

For the left piece, the internal field travels from the newly created S face towards the original N end.

For the right piece, it travels from the original S end towards the newly created N face.

Each piece therefore has its own closed magnetic field pattern.

Question 3

An investigator wants to test whether the magnetic field lines of a finite solenoid form closed loops.

A 500-turn solenoid is wound around a hollow, non-magnetic tube and connected to a DC power supply through a switch.

The left end of the solenoid is known to be N, and the right end is S.

A small compass is available.

(a) Describe how the investigator could use the compass to map the magnetic field inside and outside the solenoid.

(b) Predict the direction in which the north end of the compass points when placed:

• Inside the solenoid near its centre.
• Outside the solenoid, above its midpoint.

(c) Explain why observing the compass at only one position would be insufficient to establish the complete field pattern.

Solution 3

The compass points towards the left inside the solenoid and towards the right above the solenoid. Mapping both regions reveals the opposite directions of the internal and external fields.

(a) Describe the experimental method.

First, connect the solenoid to the DC power supply through the switch.

Close the switch and allow the current to become steady.

Place the compass inside the central bore of the solenoid. Record the direction of its north-seeking end.

Move the compass to a position outside the solenoid, above its midpoint, and record the new direction.

Repeat these measurements at several positions along the bore and around the outside of the coil.

Join the recorded directions smoothly to construct a representation of the magnetic field.

(b) Predict the compass directions.

Inside the solenoid, the magnetic field travels from S to N.

Since N is on the left, the compass points left.

Outside the solenoid, the magnetic field travels from N to S.

Above the coil, the compass points right.

Therefore:

(c) Explain why multiple measurements are necessary.

A compass measures the local magnetic field direction at one position.

A single observation cannot establish the complete shape of the magnetic field.

By recording directions at multiple positions, the investigator can follow the field from the interior of the solenoid through the external region.

The change from S-to-N inside to N-to-S outside demonstrates the continuous return path.

This is stronger evidence for the closed-loop pattern than simply observing a compass deflection at one point.

Question 4

A straight conducting wire carries a conventional current towards the east.

The wire is placed in a uniform external magnetic field directed towards the north.

Assume the current and external magnetic field are perpendicular.

(a) Determine the direction of the magnetic force on the wire.

(b) Both the current and the external magnetic field are then reversed. Determine the new direction of the force.

(c) Explain what happens to the magnetic field produced by the wire itself.

Solution 4

The magnetic force initially acts upwards. When both the current and external magnetic field reverse, the force remains upwards, while the wire’s own magnetic field reverses.

(a) Determine the initial force direction.

The wire carries current east, and the external magnetic field points north.

Use Fleming’s left-hand rule:

• First finger: magnetic field towards north.
• Second finger: conventional current towards east.
• Thumb: magnetic force.

The thumb points vertically upwards.

Therefore, the magnetic force acts upwards.

(b) Reverse both the current and external magnetic field.

The current now points west, and the external magnetic field points south.

The two directions have both reversed.

Using the magnetic force relationship,

\[
F=BIL\sin\theta
\]

the magnitude remains unchanged because:

• The current magnitude is unchanged.
• The magnetic field strength is unchanged.
• The angle remains \(90^\circ\).

The force direction also remains upwards.

This can be understood using the vector relationship:

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

Reversing both vectors produces:

\[
(-I\vec L)\times(-\vec B)
=
I\vec L\times\vec B
\]

The two reversals cancel in the force calculation.

(c) Explain what happens to the wire’s own magnetic field.

The wire’s own magnetic field depends on the direction of its conventional current.

Since the current reverses, the magnetic field around the wire also reverses.

The important distinction is that the wire’s own field and the external magnetic field are different fields.

The force calculation uses the external magnetic field acting on the current-carrying wire.

A student who uses the right-hand grip rule to determine the force would be applying the wrong direction rule.

Question 5

Two long, parallel sections of conducting wire form part of a complete electrical circuit.

They are perpendicular to the page and separated by \(4.0\ \text{cm}\).

• Wire A, on the left, carries a conventional current of \(5.0\ \text{A}\) out of the page.
• Wire B, on the right, carries a conventional current of \(5.0\ \text{A}\) into the page.

A third short conducting wire, C, is positioned exactly halfway between A and B. It carries a conventional current of \(2.0\ \text{A}\) out of the page and has a length of \(0.10\ \text{m}\).

Assume the long-wire approximation applies, ignore end effects, and calculate the external magnetic field acting on C using only the fields produced by A and B.

(a) Determine the direction of the magnetic field produced by A at C.

(b) Determine the direction of the magnetic field produced by B at C.

(c) Calculate the magnitude and direction of the resultant magnetic field at C.

(d) Calculate the magnitude and direction of the magnetic force on C.

(e) The third wire is then rotated so that its current runs towards the north, parallel to the resultant magnetic field. The current magnitude and external magnetic field remain unchanged. Determine the new magnetic force.

(f) Explain why the magnetic force becoming zero does not mean that the magnetic field has disappeared. Also explain why the magnetic fields of A and B can nearly cancel far away without their field lines terminating.

Solution 5

At C, the resultant magnetic field is \(1.0\times10^{-4}\ \text{T}\) upwards. The initial magnetic force on C is \(2.0\times10^{-5}\ \text{N}\) towards the left. When C is rotated parallel to the field, its magnetic force becomes zero, but the external magnetic field remains unchanged.

(a) Determine the magnetic field direction produced by A.

Wire A carries conventional current out of the page.

Using the right-hand grip rule, the magnetic field travels anticlockwise around A.

Wire C is to the right of A.

At this position, the magnetic field produced by A points upwards.

(b) Determine the magnetic field direction produced by B.

Wire B carries conventional current into the page.

Its magnetic field therefore travels clockwise.

Wire C is to the left of B.

At this position, the magnetic field produced by B also points upwards.

This is the important part of the problem.

Although the currents in A and B travel in opposite directions, their magnetic fields at the midpoint point in the same direction.

The fields reinforce rather than cancel.

(c) Calculate the resultant magnetic field at C.

The distance from either wire to C is:

\[
r=\frac{4.0}{2}=2.0\ \text{cm}
\]

Convert to metres:

\[
r=0.020\ \text{m}
\]

For each long straight wire:

\[
B=\frac{\mu_0 I}{2\pi r}
\]

Substitute the values:

\[
\begin{aligned}
B_A&=\frac{(4\pi\times10^{-7})(5.0)}
{2\pi(0.020)}\\
&=5.0\times10^{-5}\ \text{T}
\end{aligned}
\]

The two magnetic fields point upwards, so add their magnitudes:

\[
\begin{aligned}
B_{\text{resultant}}
&=B_A+B_B\\
&=5.0\times10^{-5}
+5.0\times10^{-5}\\
&=1.0\times10^{-4}\ \text{T}
\end{aligned}
\]

Therefore,

\[
\boxed{B_{\text{resultant}}=1.0\times10^{-4}\ \text{T}}
\]

The direction is upwards.

(d) Calculate the magnetic force on C.

The current in C is out of the page, while the external magnetic field points upwards.

These directions are perpendicular.

Use:

\[
F=BIL\sin\theta
\]

Substitute:

\[
\begin{aligned}
F&=(1.0\times10^{-4})(2.0)(0.10)
\sin90^\circ\\
&=2.0\times10^{-5}\ \text{N}
\end{aligned}
\]

Therefore,

\[
\boxed{F=2.0\times10^{-5}\ \text{N}}
\]

To determine the direction, use Fleming’s left-hand rule.

The current points out of the page, and the magnetic field points upwards.

The force acts towards the left, in the direction of wire A.

(e) Determine the new magnetic force.

The third wire is now parallel to the magnetic field.

Therefore, the angle between the current and the magnetic field is:

\[
\theta=0^\circ
\]

Using:

\[
F=BIL\sin\theta
\]

we obtain:

\[
F=BIL\sin0^\circ=0
\]

Therefore,

\[
\boxed{F=0\ \text{N}}
\]

(f) Explain the physical meaning of the result.

The magnetic field has not disappeared.

The external field produced by A and B still points upwards with a magnitude of \(1.0\times10^{-4}\ \text{T}\).

The force becomes zero because the current in C is now parallel to the external field.

Magnetic force depends on the angle between the current and magnetic field, not simply on whether a field exists.

This exposes an important misconception: zero magnetic force does not necessarily mean zero magnetic field.

Now consider the fields far away from A and B.

At distances much larger than their separation, the two contributions have nearly equal magnitudes and nearly opposite directions. Their resultant is therefore much weaker than the field produced by either wire alone.

However, this is vector cancellation, not the disappearance of magnetic field lines at an endpoint.

The field lines represent the resultant magnetic field produced by the complete arrangement. They must be traced using the combined field at each position, rather than treating the circular fields around A and B as independent physical threads.

Because the two conductors are sections of a complete circuit, the overall magnetic field also includes the effects of the return paths elsewhere in the circuit.

The magnetic field can become extremely weak, but it does not acquire a magnetic beginning or ending point.

This is the deeper reason magnetic field lines form continuous paths.

08What to remember for HSC Physics

When answering a question about closed magnetic field lines, build your explanation around three connected ideas.

1. No isolated magnetic poles: Ordinary magnets have both north and south poles. Magnetic field lines cannot begin or end at these poles.

2. The direction reverses inside and outside a magnet: Outside, the field travels N to S. Inside, it returns S to N.

3. Current also produces continuous magnetic fields: Around a straight current-carrying wire, the field forms concentric circles. Around a finite solenoid, the field resembles that of a bar magnet.

Most importantly, keep the direction rules separate:

• Use the right-hand grip rule to determine the magnetic field produced by conventional current.
• Use Fleming’s left-hand rule to determine the force on a current-carrying conductor in an external magnetic field.

Once you understand why magnetic fields have no endpoints, the next useful step is learning how multiple magnetic fields combine. That is where vector addition, neutral points, and the field patterns of interacting magnets and current-carrying wires become important.