Q.Write Ampere's circuital law, with the help of this law establish an expression for the intensity of the magnetic field inside the solenoid with the number of turns and flowing current. [1+4=5] OR Describe the moving coil galvanometer under the following points:

A long current-carrying solenoid produces a uniform axial field inside, so its field lines are parallel and straight.

Each turn of a solenoid behaves like a small circular loop. When many turns are stacked closely, their fields add along the axis and largely cancel outside. The result inside a long solenoid is a nearly uniform magnetic field of magnitude

$B = \mu_0 n I$ …

Interior field of a long solenoid B = μ₀nI, option (i).

Using Ampere's circuital law for a long solenoid, the magnetic field well inside (away from the ends) is uniform and directed along the axis:

B = μ₀ n I,

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At a solenoid's end the field is half the interior value: B_end = μ₀nI/2, option (iii).

For a long solenoid, the interior field is B = μ₀nI. At the very end of the solenoid, only 'half' of the contributing turns lie on one side, and the field on the axis drops to exactly half …

Ampère's circuital law gives the axial field of a long ideal solenoid as B = μ₀nI, which contains no radius term, so B does not depend on r. Option (d).

Step 1 — apply Ampère's law to a rectangular loop, partly inside and partly outside a long ideal solenoid (a standard NCERT/CBSE Class 12 Physics derivation in Moving Charges and Magnetism).

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The field inside a solenoid is uniform and parallel to its axis.

A solenoid is a long coil of many turns. The circular fields of the individual turns add up so that, well inside a long solenoid, the resultant magnetic field is nearly uniform, strong, and directed along the axis (its direction given by the right-hand rule). Outside …

A long, tightly-wound solenoid is the standard example of a uniform magnetic field region: inside it (away from the ends), B is constant in both magnitude and direction.

Compare the field patterns:

• A straight current-carrying wire produces a field that varies as 1/r with distance and circles the wire (non-uniform).
• At the centre of a circular loop the field has a single fixed value only at that one point, not over a region. …

A current-carrying solenoid behaves like a bar magnet, with one end acting as a north pole and the other as a south pole.

When a steady current flows through a solenoid (a long, closely wound helical coil), the magnetic field lines emerge from one end and enter the other, exactly as they do for a bar magnet, and the field pattern outside the solenoid is indistinguishable from that of an equivalent bar magnet of the same magnet …

Electromagnets give a strong magnetic field only while current flows, so they are used where a switchable magnet is needed — e.g. lifting heavy iron loads in cranes.

Concept. When current passes through a solenoid wound on a soft-iron core, the core becomes strongly magnetised, producing an electromagnet. The magnetism can be switched on/off and its strength controlled by the current.

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