A bar magnet has total length 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: [2025]

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Solution

Q.

A bar magnet has total length $2 l = 20$ 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: [2025]

1 10%

2 4%

3 3%

4 5%

Ans.
(2)

Magnetic field at P, $B = \frac{μ_{0}}{4 π} \frac{m (2 l)}{d^{3}}$ , where m is the pole strength

$\Rightarrow (\frac{△ B}{B} \times 100) = (\frac{△ l}{l}) \times 100 + 3$ $| \frac{△ d}{d} |$ $\times 100$

= 1% + 3% = 4%

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