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A 505 turn circular loop coil with a diameter of 15.5 cm is initially aligned so that...

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A 505 turn circular loop coil with a diameter of 15.5 cm is initially aligned so that its plane is perpendicular to Earths's magnetic field.  In 2.77 ms the coil is rotated 90.0 degrees so that its plane is parallel to Earth's magnetic field.  If an average emf of 0.166 V is induced in the coil, what is the value of Earth's magnetic field?

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Let Earth's magnetic field is B. Let induced emf be `epsi`  ,so

`epsi=(NDeltaphi)/(Deltat)`

`=(NBA)/(Deltat)`

`B=(epsi Deltat)/(NA)`                               (i)

where   N = no. of turns= 505

           A=  `pixx(.155/2)^2`    ,diameter is 15.5 cm ,so radius=.0775cm

          `Deltat=2.77ms=2.77xx10^(-3)sec`

         `epsi=.166 v`

`B=(.166xx2.77xx10^(-3))/(505xxpixx(.0775)^2)`

`=4.826xx10^(-5)T`

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