What is the magnitude of the induced electric field at a point near the center o

Question

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 A long, thin solenoid has 800 turns per meter and radius 2.50 cm. The current in the solenoid is increasing at a uniform rate of 33.0 A/s EValue Units Submit Request Answer Part B What is the magnitude of the induced electric field at a point 0.500 cm from the axis of the solenoid? Express your answer with the appropriate units E-1 Value Units Submit Part C What is the magnitude of the induced electric field at a point 1.00 cm from the axis of the solenoid? Express your answer with the appropriate units B-ValueUnits

Explanation / Answer

According to the Maxwell-Faraday equation, we have -

? E ? ds = - ? ?B/?t ? dS

B = (?o)(n)(I)
?B/?t = (?o)(n)(dI/dt)
?B/?t = (1.257e-6 N/A²)(800 turns/m)(+33.0 A/s)
?B/?t = 3.32e-2 T/s

and -

E[2?r] = -(?o)(n)(dI/dt)(?r²)
E = -(?o)(n)(dI/dt)(r) / 2

Part A -

At the center of the solenoid, r = 0

So, E = 0

Part B -

||E|| = (1.257e-6 N/A²)(800 turns/m)(+33.0 A/s)(5.00e-3 m) / 2
||E|| = 8.30e-5 N/C

Part C -

||E|| = (1.257e-6 N/A²)(800 turns/m)(+33.0 A/s)(1.00e-2 m) / 2
||E|| = 1.66e-4 N/C

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