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Sagot :
The magnetic moment μ of a loop that carries a current A whose cross-sectional area is A is given by:
[tex]\mu=IA[/tex]On the other hand, the torque on a current loop with magnetic moment μ placed in a magnetic field B is:
[tex]\tau=\mu B\sin\theta[/tex]Where θ is the angle between the vectors μ and B.
The direction of μ is determined using the right hand rule for the current circulating in the loop.
Draw a diagram to visualize the situation:
Since the given angle is measured from the plane of the loop to the direction of the magnetic field, and the angle θ relevant for the calculation is the complementary of the given angle, then we should use the cosine of the given angle.
Then, replace μ=IA, I=3.302A, A=0.812m^2, B=4.768T and sinθ=cos(65.562º) to find the magnitude of the torque on the loop:
[tex]\begin{gathered} \tau=\mu B\sin\theta \\ =IAB\cos(90º-\theta) \\ =(3.302A)(0.812m^2)(4.768T)\cdot\cos(65.562º) \\ =5.28887871...Nm \end{gathered}[/tex]The area has a precision of 3 significant figures. Therefore, the torque on the loop is approximately:
[tex]\tau=5.29Nm[/tex]
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