Question

a solenoid of radius r and length l has a current i= i not coswt the value of induced electric field at a distance r outside the solenoid​

Answer 1

1) a solenoid of radius r and length l has a current i= i not coswt the value of induced electric field at a distance r outside the solenoid​ is Zero.

2)Using cylindrical symmetry, the electric field integral simplifies into the electric field times the circumference of a circle.

3) Since we already know the induced emf, we can connect these two expressions by Faraday’s law to solve for the induced electric field.

Answer 2

The value of electric field at a distance r outside the solenoid is E = μonImax  ωR^2 / 2r sinωt

Explanation:

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

At a coaxial distance  r > R ∫ E⋅dl = −  dϕ / dt

E∫dl = − d/dt   (BA cos0°  )

⇒  E(2πr) = −  d / dt    (μonI)(πR^2 )

E  = −   μonR^2/2r  d /  dt  (I  max  cosωt)

E = μon Imax  ωR^2 / 2r sinωt

Hence the value of electric field at a distance r outside the solenoid is

E = μonImax  ωR^2 / 2r sinωt