A conducting wire formed in the shape of a right triangle with base b = 37 cm an

Question

A conducting wire formed in the shape of a right triangle with base b = 37 cm and height h = 59 cm and having resistance R = 2.4 ?, rotates uniformly around the y-axis in the direction indicated by the arrow (clockwise as viewed from above (loooking down in the negative y-direction)). The triangle makes one complete rotaion in time t = T = 1.5 seconds. A constant magnetic field B = 1 T pointing in the positive z-direction (out of the screen) exists in the region where the wire is rotating.

At time t = 0, the wire is positioned as shown. What is the magnitude of the magnetic flux ?1 at time t = t1 = 0.5625 s?

What is I1, the induced current in the loop at time t = 0.5625 s? I1 is defined to be positive if it flows in the negative y-direction in the segment of length h.

Please only answer these questions I have alread consulted other quetions like this on chegg and can not figure out these two questions

A conducting wire formed in the shape of a right triangle with base b = 37 cm and height h = 59 cm and having resistance R = 2.4 ?, rotates uniformly around the y-axis in the direction indicated by the arrow (clockwise as viewed from above (loooking down in the negative y-direction)). The triangle makes one complete rotaion in time t = T = 1.5 seconds. A constant magnetic field B = 1 T pointing in the positive z-direction (out of the screen) exists in the region where the wire is rotating. At time t = 0, the wire is positioned as shown. What is the magnitude of the magnetic flux ?1 at time t = t1 = 0.5625 s? What is I1, the induced current in the loop at time t = 0.5625 s? I1 is defined to be positive if it flows in the negative y-direction in the segment of length h. Please only answer these questions I have alread consulted other quetions like this on chegg and can not figure out these two questions

Explanation / Answer

period of rotation = T = 1.5 s

So, angular frequency = W = 2*pi/T = 2*pi/1.5 = 4.19 rad/s

So, with time , the component of area of triangle that will be perpendicular to magnetic field, = A*cos(Wt)

where A = area of triangle = 0.5*b*h = 0.1092 m2

So, at t = 0.5625, component of area that will be perpendicular to magneitc field = 0.1092*cos(4.19*0.5625)= -0.077

So, flux through area at (t = 0.5625)= -0.077*B = -0.077*1 = -0.077 Wb <-------------answer

At t = 0. flux = 0.1092*1 = 0.1092 Wb

So, change of flux = -0.077-0.1092 = -0.1862 Wb

So, emf generated,E = change of flux/time = -0.1862/0.5625 = 0.331 V

So, I1 = E/R = 0.331/2.4 = 0.138 A <-----------answer

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