Essential difference between electrostatic shielding by a conducting shell and magnetostatic shielding is due

NCERT Exemplar · Q8

Q. Essential difference between electrostatic shielding by a conducting shell and magnetostatic shielding is due to

(a) electrostatic field lines can end on charges and conductors have free charges.

(b) lines of B can also end but conductors cannot end them.

(d) shells of high permeability materials can be used to divert lines of B from the interior region.

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Concept understanding — Magnetic Poles

Magnetic Poles: The Intuition First

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 …

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 $m_1$ and $m_2$ , separated by distance $r$ , is:

F = \frac{\mu_0}{4\pi} \cdot \frac{m_1 m_2}{r^2}

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 $1/r^2$ (inverse square law)
- Is proportional to the product of pole strengths
- Depends on the medium (via $\mu_0$ , the permeability of free space)
Mathematical analogy: The magnetic field $B$ at distance $r$ from a single pole $m$ is:

B = \frac{\mu_0}{4\pi} \cdot \frac{m}{r^2}

This comes from Gauss's law for magnetism applied to a point source.

Force derivation: The force on pole $m_2$ in the field of pole $m_1$ is:

F = m_2 \cdot B_1 = m_2 \cdot \left( \frac{\mu_0}{4\pi} \cdot \frac{m_1}{r^2} \right)

Hence:

F = \frac{\mu_0}{4\pi} \cdot \frac{m_1 m_2}{r^2}

Key insight: The $1/r^2$ dependence is not arbitrary — it follows from the geometry of 3D space (flux spreads over a sphere of area $4\pi r^2$ ).

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 = \frac{\mu_0}{4\pi} \cdot \frac{2m l}{(x^2 - l^2)^2}

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 $(x - l)$ :

B_N = \frac{\mu_0}{4\pi} \cdot \frac{m}{(x - l)^2} \quad \text{(away from north)}

Field from south pole at distance $(x + l)$ :

B_S = \frac{\mu_0}{4\pi} \cdot \frac{m}{(x + l)^2} \quad \text{(toward south)}

Net field (both along same direction on axis):

B = B_N - B_S = \frac{\mu_0 m}{4\pi} \left[ \frac{1}{(x - l)^2} - \frac{1}{(x + l)^2} \right]

Simplify using algebra:

\frac{1}{(x - l)^2} - \frac{1}{(x + l)^2} = \frac{4xl}{(x^2 - l^2)^2}

Therefore:

B = \frac{\mu_0}{4\pi} \cdot \frac{4mxl}{(x^2 - l^2)^2}

But for a bar magnet, the magnetic moment is $\vec{M} = m \cdot (2l)$ (pole strength × separation). So $2ml = M$ , giving:

B = \frac{\mu_0}{4\pi} \cdot \frac{2Mx}{(x^2 - l^2)^2}

Key insight: The field is not simply $1/r^2$ because we have two poles — the net effect is a dipole field, which falls off as $1/r^3$ at large distances.

4. The Far-Field Approximation (Dipole Formula)

For $x \gg l$ (far from the magnet), $x^2 - l^2 \approx x^2$ , so:

B \approx \frac{\mu_0}{4\pi} \cdot \frac{2M}{x^3}

Why $1/x^3$ ?

A single pole gives $1/r^2$ …

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Electrostatic shielding is perfect because free charges (true, isolatable sources of field) can rearrange to cancel the field exactly inside a conductor. Magnetic shielding is only ever partial, because magnetic monopoles do not exist - a high-permeability shell can only redirect field lines around the interior, never cancel them. This is exactly stem option (d).

The root cause: monopoles vs. dipoles

Electric field lines can begin and end on individual (isolatable) charges. A conducting shell has free charges that migrate until the field inside is exactly zero - this is why electrostatic shielding is perfect, for any shape of shell and any external field.

Magnetic field lines, by contrast, never begin or end anywhere - there are no isolated magnetic "charges" (monopoles). Every field line forms a closed loop. So there is no free "magnetic charge" available to rearrange and cancel an external field. The best a material can do is offer field lines an easier path to follow - a low-reluctance detour - around the region you want to protect.

What a high-permeability shield actually does

A shell of a high-permeability material (like soft iron, $\mu_r\gg1$ ) placed in an external field $\vec{B}_0$ becomes strongly magnetised. The field lines are strongly attracted into the shell material itself (since it is "easier" for them to run through a high- $\mu$ medium), so most of the flux is diverted through the shell wall, leaving a much-weakened - but never exactly zero - field in the cavity inside.

Checking the options

(a) electrostatic field lines can end on charges, and conductors have free charges - this is true as a description of the electric case, but it is not, by itself, the essential difference the question is asking about (it doesn't mention the magnetic side at all).
(b) "lines of B can also end, but conductors cannot end them" - false: lines of $\vec{B}$ never end on anything, conductor or not; this misstates the basic fact about magnetic field lines. …

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Q.Essential difference between electrostatic shielding by a conducting shell and magnetostatic shielding is due to

Concept understanding — Magnetic Poles

Magnetic Poles: The Intuition First

The Two Types of Poles

The Precise Statement

A Common Confusion (Watch Out)

Why This Matters …

Why this formula?

Magnetic Poles: Why the Key Formulas Hold

1. What Is a Magnetic Pole?

2. The Key Formula: Force Between Two Magnetic Poles

Why this form?

3. The Magnetic Field of a Bar Magnet (Two Poles)

Why this form?

4. The Far-Field Approximation (Dipole Formula)

Why $1/x^3$ ?

The root cause: monopoles vs. dipoles

What a high-permeability shield actually does

Checking the options

Method: Comparing Electrostatic and Magnetostatic Shielding

Steps

Q.Essential difference between electrostatic shielding by a conducting shell and magnetostatic shielding is due to

The root cause: monopoles vs. dipoles

What a high-permeability shield actually does

Checking the options

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