The expression for the induced current i(t) as a function of time is; I = 20πr²(0.02 + 0.020t)/R
We know that formula for EMF is;
E = d∅/dt
E dt = d∅
Thus;
E∫dt = ∫d∅ ----(eq 1)
We are given the magnetic field as; B = 0.020t + 0.010t²
Thus;
∅ = (0.020t + 0.010t²) * πr²
Putting (0.020t + 0.010t²) * πr² for ∅ in eq 1 and integrating gives us the induced current as;
I = 20πr²(0.02 + 0.020t)/R
Complete question is;
5.0-cm-diameter coil has 20 turns and a resistance of 0.50Ω. A magnetic field perpendicular to the coil is B=0.020t+0.010t^2, where B is in tesla and t is in seconds. Find an expression for the induced current I(t) as a function of time.
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