A long solenoid carries a steady current. Its interior is then completely filled with a core of magnetic susceptibility \( \chi \), the current being kept the same. Consider the following statements:
(A) The magnetic intensity H inside the solenoid does not change when the core is put in.
(B) With the core, the magnetic field B inside the solenoid is \( (1+\chi) \) times its value without the core.
(C) The magnetisation of the core is \( \chi \) times the magnetic intensity H.
(D) If the core is diamagnetic, the magnetic field B inside the solenoid becomes slightly larger than its value without the core.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (C) only
Inside a core the total field has two parts. One is the magnetic intensity H, set up by the current in the windings. The other is the magnetisation M of the core material. Together they give \( B=\mu_0(H+M) \), with \( M=\chi H \).
(A) The magnetic intensity H inside the solenoid does not change when the core is put in. — True. H depends only on the windings and the current through them (\( H=nI \)). Neither changes, so H stays the same.
(B) With the core, the magnetic field B inside the solenoid is \( (1+\chi) \) times its value without the core. — True. Without the core \( B_0=\mu_0H \). With the core:
\( \begin{aligned} B &= \mu_0(H+\chi H) \\ &= \mu_0(1+\chi)H \\ &= (1+\chi)B_0 \end{aligned} \)
(C) The magnetisation of the core is \( \chi \) times the magnetic intensity H. — True. This is the relation \( M=\chi H \) that defines the magnetic susceptibility.
(D) If the core is diamagnetic, the magnetic field B inside the solenoid becomes slightly larger than its value without the core. — False. For a diamagnetic core \( \chi \) is negative, so \( 1+\chi\lt1 \) and the field inside becomes slightly smaller.
NCERT (2026-27):
Magnetisation and Magnetic Intensity – “… We have partitioned the contribution to the total magnetic field inside the sample into two parts: one, due to external factors such as the current in the solenoid. This is represented by H. The other is due to the specific nature of the magnetic material, namely M. The latter quantity can be influenced by external factors. This influence is mathematically expressed as”
\( M=\chi H \)\( \qquad (5.13) \)
“where χ, a dimensionless quantity, is appropriately called the magnetic susceptibility. … we obtain,”
\( B=\mu_0(1+\chi)H \)\( \qquad (5.14) \)
Diamagnetism – “… The field lines are repelled or expelled and the field inside the material is reduced. …”