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Question

# (a) By how many percent is the torque of a motor decreased if its permanent magnets lose 5.0% of their strength? (b) How many percent would the current need to be increased to return the torque to original values?

Solution

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a) Since the magnitude of the torque on a loop of area {A} that carries a current {I} whose area vector makes an angle {$\theta$} with a magnetic field of density {B} is given by the equation:

$\left| \vec{\tau}\right| =B I A \sin{\theta}$

So the ratio of the final torque on the loop after the decrease in B to the initial value is:

\begin{align*} \dfrac{| \vec{\tau}_{f}|}{| \vec{\tau}_{i} |} &=\dfrac{B_f (I A \sin{\theta})}{B_i (I A \sin{\theta})}\\ &=\dfrac{B_f}{B_i}\\ &=0.95 \end{align*}

Therefore, the magnitude of the torque on the motor decreases by $5\%$ too, as expected for any two linearly related variables.

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