In working with the deflection magnetometer, the proportional error will be minimum when the deflection is :

^{o}

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^{o}

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^{o}

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^{o}

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Solution

The correct option is D 45 $^{o}$
From the Formula,
$B_{H} = B cot θ$
To get the sensitivity, we differentiate the above equation and write
$d B_{H} = - B c o s e c^{2} θ d θ$
So we get $\frac{d B_{H}}{B_{H}} = \frac{- c o s e c^{2} θ d θ}{cot θ} = \frac{- 2 d θ}{sin 2 θ}$
To minimize the error, we have to minimize the absolute value of $\frac{d B_{H}}{B_{H}}$
That will happen only when $sin 2 θ = 1$ i.e. $θ = 45^{\circ}$

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