Question 26

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 :

$$\text{Given: } \frac{\Delta l}{l} = 1\%,\ \frac{\Delta d}{d} = 1\%$$

$$B \propto \frac{l}{d^3}$$

$$\frac{\Delta B}{B} = \frac{\Delta l}{l} + 3\left(\frac{\Delta d}{d}\right)$$

$$\frac{\Delta B}{B}\% = 1\% + 3(1\%) = 4\%$$

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