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A solenoid of a radius R wound with n turns per unit lengthcarries a current given by I = I0e −βt, where t is the time and β > 0.What are the magnitude and direction of the induced electric field justoutside the solenoid?

Question

A solenoid of a radius R wound with n turns per unit length
carries a current given by I = I0e −βt, where t is the time and β > 0.
What are the magnitude and direction of the induced electric field just
outside the solenoid?

check_circleAnswer
Step 1

The magnetic field due to solenoid is,

B(t) nl ()
= 4,nle
-Bt
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B(t) nl () = 4,nle -Bt

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Step 2

From Faraday’s law, the magnitude of induced Electric field is related to the magnitude of change in magnetic flux as,

Ввd4
(1)
dt
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Ввd4 (1) dt

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Step 3

Here, the integral is over the entire path which is of radius r. The radius r is g...

BA
-(4,nleR)
= Tu,lRe
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BA -(4,nleR) = Tu,lRe

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