The magnetic flux through a coil perpendicular to its plane is varying according to the relation - φ = (4t3 + 5t2 + 8t + 5 ) weber Calculate the induced current through the coil at t = 2 second, if the resistance of the coil.

Dear Student ,
Here in this case the magnetic flux through a coil perpendicular to its plane is varying according to the relation ,
φ=4t3+5t2+8t+5
As you have not provided us the resistance of the coil so we are taking that the resistance of the coil be R.
So the ,potential difference is , 
e=-dφdt=-ddt(4t3 + 5t2 + 8t + 5 )=-12t2-10t-8
Therefore , induced current through the coil at time t= 2 second is ,
it=2 sec=eRt=2 sec=-12t2-10t-8Rt=2 sec=-48-20-8R=-76 RA    Here the negative sign indicates that the induced current will oppose the factor producing it.
Regards
 

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