A 50-cm-long metal rod rotates about the z-axis at 180 revolutions per minute, w

Question

A 50-cm-long metal rod rotates about the z-axis at 180 revolutions per minute, with end 1 fixed at the origin. Determine the induced emf, V_12 due to motion if B = z3 Times 10^-4 T. An inductor is formed by winding N turns (in the x-y plane) of a thin conducting wire into a circular loop of radius a. The inductor loop is in the plane with its center at the origin, and connected to a resistor R. In the presence of a magnetic field B = B_o (y2 + z3)sin omega t, where co is the angular frequency, find the magnetic flux, Phi, linking a single turn of the inductor. the emf, given that N = 10, B_o = 0.2 T, a = 10 cm, and omega = 10^3.

Explanation / Answer

10. Given: Length of rod (L) = 50 cm = 0.5 m ; frequency of revolution (f) = 180/60 = 3 rev/s

and Magnetic field (Bz) = 3*10-4 T

Hence angular frequency of revolution () = 2f = 2*3.14*3 = 18.84 rad/s

Induced emf produced in this case is = Bz**L2/2 = 3*10-4*18.84*0.5*0.5/2= 7.06*10-4 V

11. Given: Bz = 3*B0*sin(t) ; Number of turms of inductor = N ; area of circular coil (A) = *a2

(a) Hence flux in a sigle loop is given by () = Bz*A = 3**a2*B0*sin(t)

(b) Now total magnetic flux through the loop would be (tot) = N*3**a2*B0*sin(t)

therefore emf induced = dtot/dt = N*3**a2*B0**cos(t) = 10*3*3.14*0.1*0.1*0.2*103*cos(1000t)

= 188.4*cos(103t)

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