Two similar magnetic poles having pole strengths in the ratio 1 : 4 are placed 6 cm apart. The distance from a smaller pole in strength where net magnetic field is zero will be:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2 cm
The magnetic field of a pole of strength \( m \) at distance \( r \) follows an inverse-square law, like the field of a point charge.
\( \displaystyle B = \frac{\mu_0}{4\pi}\,\frac{m}{r^{2}} \)
The poles are similar (like) poles, so between them their fields point in opposite directions. The null point lies on the line joining them, nearer the weaker pole. Let it be at \( x \) from the smaller pole \( m \); it is then at \( 6 - x \) from the pole \( 4m \).
\( \displaystyle \frac{m}{x^{2}} = \frac{4m}{(6 - x)^{2}} \)
\( \displaystyle \left(\frac{6 - x}{x}\right)^{2} = 4 \;\Rightarrow\; \frac{6 - x}{x} = 2 \)
\( \displaystyle 6 - x = 2x \;\Rightarrow\; x = 2\,\mathrm{cm} \)
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
Bar Magnet as an Equivalent Solenoid – “… Some textbooks assign a magnetic charge (also called pole strength) +qm to the north pole and –qm to the south pole of a bar magnet of length 2l, and magnetic moment qm(2l). The field strength due to qm at a distance r from it is given by
\( \displaystyle \frac{\mu_0 q_m}{4\pi r^2} \)”