At one place on earth, the resultant magnetic field is 0.25 G and the angle of dip is \( 45^\circ \). The horizontal component of earth's magnetic field will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.18 G
The angle of dip \( \delta \) is the angle that the earth's total field \( B_E \) makes with the horizontal. So the horizontal component is the projection of \( B_E \) on the horizontal.
\( \displaystyle H_E = B_E\cos\delta \)
\( \displaystyle H_E = 0.25\,\mathrm{G} \times \cos 45^\circ = 0.25 \times 0.707 = 0.177\,\mathrm{G} \approx 0.18\,\mathrm{G} \)
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):
Magnetic Declination and Dip – “… Thus, dip is the angle that the total magnetic field BE of the earth makes with the surface of the earth. … The total magnetic field at P can be resolved into a horizontal component HE and a vertical component ZE. … Representing the verticle component by ZE, we have
\( \displaystyle Z_E = B_E \sin I \qquad [5.10(a)] \)
\( \displaystyle H_E = B_E \cos I \qquad [5.10(b)] \)”