A 4.0-cm-diameter loop with resistance 0.19 around a 2.0-cm-diameter solenoid. T

Question

A 4.0-cm-diameter loop with resistance 0.19 around a 2.0-cm-diameter solenoid. The solenoid is 15 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)

Part A

Find the current in the loop at t = 0.5s.

Express your answer as an integer and include the appropriate units.

Part B

Find the current in the loop at t = 1.5s.

Express your answer to two significant figures and include the appropriate units.

Part C

Find the current in the loop at t = 2.5s.

Express your answer as an integer and include the appropriate units.

MasteringPhysics: Homework 11 (Ch. 30 & 32) - Google Chrome Secure l https://session.masteringphysics.com/myct/itemView?offset=next&assignmentProblemID;=82886545 rk 1 Problem 30.46 Resources

Explanation / Answer

magnetic field produced by solenoid B = uo*(N/L)*I

magnetic flux phi = B*A

A = effective area = pi*r^2

r = radius of solenoid = 2/2 = 1 cm = 0.01 m

mganetic flux = uo*(N/L)*I*pi*r^2

induced emf = rate of change in flux

emf = uo*(N/L)*pi*r^2*(dI/dt)

current I = emf/R

R = resistance

I(t) = (uo*(N/L)*pi*r^2/R)*(dI/dt)

I(t) = (4*pi*10^-7*(100/0.15)*pi*0.01^2/0.19)*(dI/dt)

I(t) = 1.38*10^-6*(dI/dt)

part(A)

at t = 0.5

current I is constant

dI/dt = 0

current in the loop I(0.5) = 0

=======================

part B

at t= 1.5s

slope dI/dt = (20/0.5) = 40 A

I(1.5) = 1.38*10^-6*40

I(1.5) = 5.52*10^-5 A

=========================

part(c)

at t = 2.5

dI/dt = 0

I(2.5) = 0

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