The force exerted by a magnetic field on a wi | vedclass

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(A) Given the formula for force: $|F| = I L |B|$.Since the plot of $|F|$ versus $L$ is a straight line,the slope $S$ is given by $S = \frac{|F|}{L} =

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$\frac{50}{3}\%$

Vedclass · Answer

(A) Given the formula for force: $|F| = I L |B|$.Since the plot of $|F|$ versus $L$ is a straight line,the slope $S$ is given by $S = \frac{|F|}{L} = I |B|$.Therefore,the magnetic field is $B = \frac{S}{I}$.The relative error in $B$ is given by the formula: $\frac{\Delta B}{B} = \frac{\Delta S}{S} + \frac{\Delta I}{I}$.Given $S = (10 \pm 1) 	imes 10^{-5} \ T$ and $I = (15 \pm 1) \ mA = (15 \pm 1) 	imes 10^{-3} \ A$.Substituting the values: $\frac{\Delta B}{B} = \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{5}{30} = \frac{1}{6}$.The percentage error in $B$ is $\frac{\Delta B}{B} 	imes 100 = \frac{1}{6} 	imes 100 = \frac{50}{3} \%$.

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