Find an expression for the induced current i(t) as a function of time.

A 5.0-cm-diameter coil has 20 turns and a resistanceof 0.50 ohms. A magnetic field perpendicular to the coil is B =0.02t + 0.010t^2, where B is in tesla and tis in seconds. Find an expression for the induced current I(t)as a function of time.

Answer

(I)=((N*pi*r^2)/R)*dB/dt
N=number of turns
r=half your diameter in meters
R=the resistance
dB/dt=is the derivative of the field in relation tot=.02+.02t
I(t)  =.025{cdot}{pi}{cdot}left(.02+.02tright)  rm A

According to Faradays law, the relation between the induced emf and magnetic field is given as: dt -Nd(B.A) dt Here, D is thThe magnetic field acting is time differentiated: d(B) N (A) dt I R d(0.020+0.010) N (zR)| dt R d(0.02t+0.0102)T 20 (7(2.5x10

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