A 4.0-cm-diameter loop with resistance 0.13 Ohm around a 2.0-cm-diameter solenoi

Question

A 4.0-cm-diameter loop with resistance 0.13 Ohm around a 2.0-cm-diameter solenoid. The solenoid is 13 cm long, has 100 turns, and carries the current shown in the graph. A positive current is cw when seen from the left. (Figure 1) Find the current in the loop at t = 0.5s. Express your answer as an integer and include the appropriate units. Find the current in the loop at t = 1.5s. Express your answer to two significant figures and include the appropriate units. Find the current in the loop at t = 2.5s. Express your answer as an integer and include the appropriate units.

Explanation / Answer

magnetic field in the solenoid = B = uo*n*I = uo*N/L*I

N = 100

L = 0.11 m

flux through the loop = B*A

emf induced = rate of chang ein flux

e = (d/dt)*(B*A)

A = area of cross section of loop containig flux

e = uo*N/L*A*dI/dt

current in the loop = i = e/R

i = uo*N/L*pi*r^2*dI/dt*(1/R)

A)

at t = 0.5 the current in the solenoid is not changing dI = 0

i = 0

B)

between t = 1 s to t = 1.5 s current changed from 20 A to 0 A

dI = 20

dt = 0.5

i = uo*N/L*pi*r^2*dI/dt*(1/R)

i = (4*pi*10^-7*(100/0.11)*pi*0.01^2*(20/0.5)*(1/0.13))

i = 0.00011A = 0.11 mA

__

C)

at time t = 2.5 s

the current is constant dI = 0

i = 0

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