Question

10.
A solenoid of radius R and length L has a current
1 = 1, coswt. The value of induced electric field at
a distance of r outside the solenoid, is :
(1) HonlooR?
-sinot
2r
(2) Honloor
-sinot
(3) MonleRsinot
2r
(4) Zero​

Answer 1

Answer:

(4) Zero is the correct answer

Answer 2

The induced electric field at a distance is $\dfrac{\mu_{0}nI_{max}\omega R^2}{2r}\sin\omega t$

(A) is correct option.

Explanation:

Given that,

Current $I=I\cos\omega t$

Distance =r

Radius = R

Length = L

The changing magnetic flux inside the solenoid, induces the electric field

A a distance r>R

We need to calculate the induced electric field at a distance

Using formula of electric field

$\int{E\cdot dl}=-\dfrac{d\phi}{dt}$

Put the value into the formula    

$E\int{dl}=-\dfrac{d}{dt}(\mu_{0}nI)(\pi R^2)$

$E(2\pi r)=-\dfrac{d}{dt}(\mu_{0}nI)(\pi R^2)$

$E=\dfrac{-\mu_{0}nR^2}{2r}\times\dfrac{d}{dt}(I_{max}\cos\omega t)$

$E=\dfrac{\mu_{0}nI_{max}\omega R^2}{2r}\sin\omega t$

Hence, The induced electric field at a distance is $\dfrac{\mu_{0}nI_{max}\omega R^2}{2r}\sin\omega t$

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Topic : electric field

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