Two questions PLZ be specific Thank you A Dangling Loop The rectangular loop sho

Question

Two questions

PLZ be specific

Thank you

A Dangling Loop The rectangular loop shown (Figure 1) is made of wire of linear mass density 0.16 g per centimeter. It is free to rotate (frictionlessly) about an axis along side ab, and the current in the wire is 8.5 A in the direction indicated. Figure 1 of 1 6.00 cm 30.0 8.00 Part A determine what its magntidue must be if the plane of the loop makes a 30.0 angle external magnetic field parallel to the yaxis, Express your answer using two significant figures Submit My Answers Give Up Part B Which way parallel to the y-axis must this external field be? -y direction O +y-direction Submit My Answers Give Up h he y2-plane

Explanation / Answer

Part 1: Dangling Loop:

The torque about the z axis due to gravity force is in -z direction hence the torque due to magnetic field must be in + z direction. So by observation we can see here that the direction of magnetic field must be in +y direction. The magnitude of torque due to gravity force will be mg*(8/2)*10^-2*sin(30 deg) = (0.16*10^-3*8*10^-2)*9.81*(8/2)*10^-2*sin(30 deg)*2+(0.16*10^-3*6*10^-2)*9.81*(8)*10^-2*sin(30 deg) = 8.79*10^-6 Nm

The magnitude of torque due to magnetic field = mu X B = IA*B*sin(60 deg) = 8.5*B*48*10^-4*sin(60 deg) = 0.035B

hence 0.035B =  8.79*10^-6 => B = 2.49*10^-4 T.

Part B:

The force due to magnetic field F = IBL sin(theta) = 6.4*0.31*0.2 = 0.397 N

Equating the horizontal component, we get,

k*delta_x = F*cos(37 deg) = 0.32 N

hence delta_x = 0.068 m

so stored energy = 0.5*k*delta_x^2 = 0.5*4.7*0.068^2 = 0.011 J.

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