What Determines the Electric Field Magnitude at Half the Radius of a Solenoid?

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SUMMARY

The magnitude of the electric field at a distance of R/2 from the axis of a long solenoid can be calculated using the formula μ0(dI/dt)(N/L)R/4. This formula incorporates the rate of change of current (dI/dt), the number of windings per unit length (N/L), and the radius (R) of the solenoid. The confusion regarding the denominator of 4 arises from the specific geometry of the electric field produced by the changing magnetic field within the solenoid. Understanding this derivation is crucial for accurate calculations in electromagnetic theory.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically Faraday's Law of Induction.
  • Familiarity with solenoid characteristics, including radius (R), length (L), and number of windings (N).
  • Knowledge of the relationship between electric fields and changing magnetic fields.
  • Basic calculus to comprehend the rate of change of current (dI/dt).
NEXT STEPS
  • Study Faraday's Law of Induction in detail.
  • Learn about the derivation of electric fields from magnetic fields in solenoids.
  • Explore the concept of displacement current and its implications in electromagnetic fields.
  • Investigate practical applications of solenoids in electrical engineering.
USEFUL FOR

Students of physics, electrical engineers, and anyone interested in understanding the principles of electromagnetism and solenoid behavior in electric fields.

freddy13
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Homework Statement



A long solenoid of radius R, length L (which
is much longer than R), number of windings
N, has a current I that is changing in time at
a rate (dI/dt). What is the magnitude of the
electric eld a distance R=2 from the axis of
the solenoid?

Homework Equations



μ0(N/L)I

The Attempt at a Solution



I thought I had this completely right until I get to the R/2 Part. if you just throw the R/2 part into the equation, then you get the B field I believe, but the answer is: μ0(dI/dt)(N/L)R/4.

I am not seeing where the 4 in the denominator comes from unless we had some kind of divisible action of R going on somewhere, or something. Not really sure how to proceed!
 
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freddy13 said:

Homework Statement



What is the magnitude of the
electric eld a distance R=2 from the axis of
the solenoid?

!

Start by stating the problem correctly. What do you mean by "R=2"? Did you mean R/2? 2R?
 

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