A bar magnet has total length 2l = 20 units and the field point P is… | JEE Main 2025 (28 Jan, Shift 2 (one Or More Correct))

Q6JEE Main 2025 · 28 JAN · SHIFT 2 (One or more correct)Difficult

Field of a Magnet & Magnet in a Uniform Field

A bar magnet has total length $2l = 20$ units and the field point P is at a distance $d = 10$ units from the centre of the magnet. If the relative uncertainty of length measurement is $1\%$ , then uncertainty of the magnetic field at point P is:

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Answer: (c)

P is on the equatorial line: $B = \frac{\mu_0}{4\pi}\frac{M}{(d^2+l^2)^{3/2}}$ (treat $M$ as given).
$\frac{\Delta B}{B} = \frac{3}{2}\cdot\frac{2d\,\Delta d + 2l\,\Delta l}{d^2+l^2}$
$d = l = 10$ , $\Delta d = \Delta l = 1\%$ of 10 $= 0.1$ : $\frac{\Delta B}{B} = \frac{3}{2}\cdot\frac{2 + 2}{200} = 0.03$
So the answer is (c) 3%.

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Field of a Magnet & Magnet in a Uniform Field question from JEE Main 2025 (28 Jan, Shift 2 (one Or More Correct))

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