Question

oSUniPhys1 30.1.P.029 My Notes 0/1 points Previous Answers The accompanying figure shows a rectangular coil consisting of 30 closely spaced turns that has a resistance of 9.0 . The magnetic field at all points inside the coil varies according to B Boe-at, where B 0.20 T and a 200 s-1 = В х х х х х 2.0 cm х х - 5.0 cm What is the current induced in the coil (in A) at the following times? (Enter the magnitudes.) (a) 0.001 s X A (b) 0.002 s XA (c) 2.0 s A X

Answer 1

given
N = 30 turns
R = 9 ohms
A = 5*2 = 10 cm^2 = 10*10^-4 m^2
B = Bo*e^(-alfa*t)
Bo = 0.2 t
alfa = 200 s^-1

induced emf in the loop, induced emf = -N*A*dB/dt

= -N*A*Bo*e^(-lafa*t)*(-alfa)

= N*A*alfa*Bo*e^(-alfa*t)

induced current, I = induced emf/R

= N*A*alfa*Bo*e^(-alfa*t)/R

a) at t = 0.001 s

I = N*A*alfa*e^(-alfa*t)/R

= 30*10*10^-4*200*0.2*e^(-200*0.001)/9

= 0.109 A <<<<<<<<<<<<-------------------Answer

b) at t = 0.002 s

I = N*A*alfa*e^(-alfa*t)/R

= 30*10*10^-4*200*0.2*e^(-200*0.002)/9

= 0.0894 A <<<<<<<<<<<<-------------------Answer

c) at t = 2.0 s

I = N*A*alfa*e^(-alfa*t)/R

= 30*10*10^-4*200*0.2*e^(-200*2.0)/9

= 0.00 A <<<<<<<<<<<<-------------------Answer