Along solenoid of radius R and n turns per unit length carries a time-varying current I = I0 cos(omega t). What is the magnitude of the induced electric field at a distance r from the axis, where r is less than R?

A. 12 _0 n I_0 r ( t) — Using Faraday's law in integral form, the line integral of the electric field around a circular path of radius r equals the negative rate of change of magnetic flux through that path. The magnetic field inside the solenoid is B = mu0 n I.

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$Along solenoid of radius R and n turns per unit length carries a time-varying current I = I_{0} cos (ω t) . What is the magnitude of the induced electric field at a distance r from the axis, where r < R ?$

A. $\frac{1}{2} μ_{0} n I_{0} ω r sin (ω t)$
B. $μ_{0} n I_{0} ω r sin (ω t)$
C. $\frac{1}{4} μ_{0} n I_{0} ω r sin (ω t)$
D. $\frac{μ _{0} n I _{0} ω R ^{2}}{2 r}$

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Correct answer: A — $\frac{1}{2} μ_{0} n I_{0} ω r sin (ω t)$

Solution

\oint E \cdot d l = - \frac{d}{d t} \int B \cdot d A . Thus E (2 π r) = - \frac{d}{d t} (μ_{0} n I_{0} cos (ω t) π r^{2}) . Solving for E gives \frac{1}{2} μ_{0} n I_{0} ω r sin (ω t) .

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Along solenoid of radius R and n turns per unit length carries a time-varying current I=I0​cos(ωt). What is the magnitude of the induced electric field at a distance r from the axis, where r<R?

Solution

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More Electromagnetic Induction practice questions

$Along solenoid of radius R and n turns per unit length carries a time-varying current I = I_{0} cos (ω t) . What is the magnitude of the induced electric field at a distance r from the axis, where r < R ?$