Q.S is the surface of a lump of magnetic material.
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Magnetic Field Lines
A magnet or a current-carrying wire fills the space around it with a magnetic field. We cannot see this field, so we picture it using magnetic field lines — continuous curves that map both the direction and the strength of the field at every point.
What a field line represents
The tangent to a field line at any point gives the direction of the magnetic field B there. If you place a tiny compass needle at that point, it aligns along the tangent, its north pole pointing the way the line runs. The density of the lines (how closely packed they are) represents the magnitude of B: crowded lines mean a strong field, widely spaced lines mean a weak field.
Key properties (exam essentials)
- Outside a magnet the lines run from the north pole to the south pole, but they are continuous closed loops — inside the magnet they run south to north, so every line closes on itself.
- Two field lines never intersect. If they did, a compass at the crossing point would have to point in two directions at once, which is impossible.
- Lines are crowded where the field is strong (near the poles) and spread out where it is weak.
- They form smooth, continuous curves with no free ends.
The fact that magnetic field lines always close on themselves is deep: it means there are no isolated magnetic poles (monopoles). This is Gauss's law for magnetism:
∮B⋅dA=0
The net magnetic flux through any closed surface is zero — every line that enters the surface also leaves it.
Contrast with electric field lines
Electric field lines start on positive charges and end on negative charges — they are open curves. Magnetic field lines have no such start or end; they are always closed loops. This single difference reflects that isolated electric charges exist, but isolated magnetic poles do not.
Uniform field …
Why this formula?
Magnetic Field Lines
A magnetic field line is an imaginary curve we draw to picture an invisible field. Its purpose is to encode two things at once: the direction of the field B (the tangent to the line at any point) and the strength of the field (how densely the lines are packed). They are a map, not physical objects.
The four defining rules
1. The tangent gives the field direction. At every point, B points along the tangent to the field line through that point. A compass needle placed on the line aligns with it.
2. Field lines form closed loops. Unlike electric field lines, which begin and end on charges, magnetic field lines never start or stop. This is Gauss's law for magnetism:
∮B⋅dA=0
The net flux through any closed surface is zero because isolated magnetic poles (monopoles) do not exist — every north pole is paired with a south pole. So for a bar magnet the lines emerge from the north pole outside, curve around to the south pole, and continue through the interior of the magnet back to the north, closing the loop.
3. Field lines never cross. If two lines crossed, the tangent — and hence B — would have two directions at that point. Since the field has a single, unique direction everywhere, crossings are impossible. …
The field B obeys ∇⋅B=0 everywhere, so its normal component is continuous and its lines are always continuous (closed) across the surface S (a correct, b wrong). But H=B/μ0−M, and M jumps to zero outside the material, so the surface acts like a magnetic-pole layer where H's normal component is discontinuous — the H lines cannot all be continuous (d c …
Because ∇⋅B=0 always, B-lines are continuous across the surface of a magnetic lump. But H is sourced by magnetic poles at that surface, so H-lines cannot all be continuous. Correct options: (a) and (d).
Concept understanding. The two magnetic fields obey
∇⋅B=0,B=μ0(H+M),∇⋅H=−∇⋅M.
The first says B has no sources or sinks: its field lines are always closed loops and its normal component is continuous across any boundary,
Bn,in=Bn,out.
Inside the material M=0; just outside M=0. So M drops abruptly across S, and this jump acts as an effective surface pole density σm=M⋅n^. From H=B/μ0−M, the normal component of H jumps:
Hn,out−Hn,in=Mn=M⋅n^.
Testing each option.
- (a) Lines of B are necessarily continuous across S (normal component continuous; B-lines are closed). Correct. …
Method: Boundary Conditions for B and H at a Material Surface
Use this method for any question asking whether field lines of B or H are continuous across the surface of a magnetised material.
Steps
Step 1: Start from the two governing relations
∇⋅B=0,H=μ0B−M
The first is universal — always true, everywhere, for any magnetic field, with no exceptions.
Step 2: Apply Gauss's law for magnetism at the boundary
Because ∇⋅B=0 never fails, the normal component of B is always continuous across any surface: Bn,in=Bn,out. So B field lines are always continuous — they close on themselves and never terminate anywhere, including at a material boundary.
Step 3: Track what happens to M across the boundary …
- KCET 2020Set A-11 markMCQQ.In a permanent magnet at room temperature (A) Magnetic moment of each molecule is zero. (B) The individual molecules have non-zero magnetic moment which are all perfectly aligned. (C) Domains are partially aligned. (D) Domains are all perfectly aligned.
›Reveal solutionSolution
A permanent magnet retains its magnetism because its microscopic magnetic domains are partially aligned, not perfectly aligned — perfect alignment would require absolute zero or an infinitely strong field.
The key to this question lies in understanding magnetic domains — tiny regions within a ferromagnetic material where the magnetic moments of atoms are already aligned. In an unmagnetised piece of iron, these domains point in random directions, so the net magnetic field cancels out. When you magnetise it (by placing it in an external field or stroking it with another magnet), the domains that happen to be aligned with the field grow at the expense of others, and some domains rotate to align partially. The result is a net magnetisation that persists even after the external field is removed — that’s what makes it a permanent magnet.
Now, at room temperature, thermal energy constantly jostles the atoms. This thermal agitation prevents perfect alignment of all domains. If every single domain were perfectly aligned, the material would be magnetically saturated — a state that requires either an extremely strong external field or cooling to near absolute zero. A permanent magnet sitting on your desk is far from that condition.
Let’s examine each option carefully.
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Option (A): “Magnetic moment of each molecule is zero.”
This is false. In a ferromagnetic material like iron, each atom (or molecule) has a permanent magnetic moment due to unpaired electrons in its d- or f-orbitals. These moments are never zero — they’re the very reason the material can be magnetic at all. What changes is the alignment of these moments, not their existence.
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Option (B): “The individual molecules have non-zero magnetic moment which are all perfectly aligned.”
This describes a perfectly saturated magnet. But at room temperature, thermal vibrations prevent perfect alignment. Even the strongest permanent magnets (like neodymium) have only about 70–90% of their domains aligned. Perfect alignment would mean every atomic moment points exactly the same way — that’s impossible at room temperature because thermal energy randomises some fraction of them.
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Option (C): “Domains are partially aligned.” …
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- KCET 2019Set A-11 markMCQQ.In a permanent magnet at room temperature (A) magnetic moment of each molecule is zero. (B) the individual molecules have non zero magnetic moment which are all perfectly aligned. (C) domains are partially aligned. (D) domains are all perfectly aligned.
›Reveal solutionSolution
In a permanent magnet at room temperature, the material is ferromagnetic and its magnetic domains are partially aligned — not perfectly aligned — because thermal agitation prevents perfect ordering. The correct option is (C).
The key to this question lies in understanding how permanent magnets work at the microscopic level. A permanent magnet is made of a ferromagnetic material (like iron, nickel, or cobalt). In such materials, individual atoms have permanent magnetic moments due to unpaired electrons. However, these moments do not act independently — they strongly interact with neighbours, causing large groups of atoms (about 1012 to 1015 atoms) to align their moments spontaneously. These groups are called domains.
Each domain is like a tiny magnet with all its atomic moments aligned. But in an unmagnetised piece, the domains themselves point in random directions, so the net magnetic field cancels out. To make a permanent magnet, we apply an external magnetic field, which causes domains that are aligned with the field to grow at the expense of others, and also rotates domain magnetisation. After the field is removed, some of this alignment remains — the material is now a permanent magnet.
Now, at room temperature, thermal energy constantly jostles the atoms. This thermal agitation prevents the domains from being perfectly aligned. Some domains will still point in directions that are not exactly along the net magnetisation. So the alignment is partial, not perfect.
Let's examine each option:
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Option (A): "Magnetic moment of each molecule is zero."
This is false. In a ferromagnetic material, each atom (or molecule) has a non-zero magnetic moment due to unpaired electrons. If the moments were zero, there would be no magnetism at all.
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Option (B): "The individual molecules have non zero magnetic moment which are all perfectly aligned."
This describes a perfectly ordered state. But at room temperature, thermal energy disrupts perfect alignment. Perfect alignment occurs only at absolute zero (0 K). At room temperature, the alignment is not perfect — it's partial.
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Option (C): "Domains are partially aligned." …
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