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ile Edit View History Bookmarks People Window Help ABC . Extended Thu 2:16 AI MasteringPhysics: MP12 Secure https://session.masteringphysics.com/myct/iter view?assignmenproblemID.90269698 MP12 Exercise 29.38 3 of8> Constants Part A A long, thin solenoid has 700 turms per meter and radius 2.50 cm. The current in the solenoid is increasing at a uniform rate of 33.0 A/s What is the magnitude of the induced electric field at a point near the center of the solenoid? Express your answer with the appropriate units. E-Value Units Submit Request Answer Part B What is the magnitude of the induced electric fieild at a point 0.500 cm from the axis of Express your answer with the appropriate units. the solenoid? E Value Units

Explanation / Answer

Given,

N = 700 ; r = 2.5 cm ; I = 33 A/s

q)We know that

E = V/d = V/2 pi r

we know that induced emf is given by:

e = -d(phi)/dt = d(BA)/dt = A(dB/dt)

B = N u0 I (for a solenoid)

e = N u0 A (dI/dt)

putting this in expression of E, we get

E = u0 N r/2 (dI/dt)

near the center, r = 0

E = 4 pi x 10^-7 x 700 x 0/2 (33) = 0 N/C

Hence, E = 0 N/C

b)r = 0.5 cm = 0.005 m

E = 4 pi x 10^-7 x 700 x 0.005/2 (33) = 7.25 x 10^-5 N/C

Hence, E(0.5 cm) = 7.25 x 10^-5 N/C

c)r = 1 cm = 0.01 m

E = 4 pi x 10^-7 x 700 x 0.01/2 (33) = 1.45 x 10^-4 N/C

Hence, E(1 cm) = 1.45 x 10^-4 N/C

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