A rectangular loop rotates with a constant angular velocity about an axis as sho

Question

A rectangular loop rotates with a constant angular velocity about an axis as shown. It makes one complete rotation in 0.04 s. The magnetic field lines are straight and parallel as shown. They are perpendicular to the axis of rotation. The lengths are c= 0.9 m and d= 3.3 m, the strength of the magnetic field is 0.05 T. The total resistance of the loop is 136 . 1) What is the magnetic flux through the loop at the instant the normal to the loop makes an angle of 0° with the magnetic field? F(09)-T-m2 2) What is the magnetic flux through the loop at the instant the normal to the loop makes an angle of 30° with the magnetic field? F(30)-T-m2 3) What is the magnetic flux through the loop at the instant the normal to the loop makes an angle of 90° with the magnetic field? F(909) 0 T-m2 4) What is the angle between the normal to the loop and the B-field when the emf in the loop is at its maximum value? --

Explanation / Answer

1)

magnetic flux = B*A*cos0

flux = 0.05*0.9*3.3*cos0 = 0.1485 T m^2

(2)

magnetic flux = B*A*cos30

flux = 0.05*0.9*3.3*cos30 = 0.1286 T m^2

(3)

magnetic flux = B*A*cos90

flux = 0.05*0.9*3.3*cos90 = 0 T m^2

(4)

maximum value = B*A

B*A = B*A* costheta

theta = 0

(5)

emf = rate of change in flux

e = (d/dt)*B*A*cos(wt)

e = B*A*sinwt*w

emax = B*A*w

maximum current I = emax/R

I = (0.05*0.9*3.3*2*pi/(136*0.04))

I = 0.171 A <<<<<-----------answer

_________________

(6)

torque = uxB

torque = I*A*B*sin90 = 0.171*0.9*3.3*0.05 = 0.0254 Nm

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