5. (10 points) A long solenoid of radius \( R \) has \( n \) turns of wire per unit length and carries a time-varying current that varies sinusoidally as \( I = I{\max} \cos \omega t \), where \( I{\max} \) is the maximum current and \( \omega \) is the angular frequency of the alternating current source (Figure 5). Please find the magnitudes of the electric field at the points on the dash circle with radius \( r \) for the cases \( r < R \) (5 points) and \( r > R \) (5 points). Assume the magnitude of the magnetic field inside the solenoid is uniform.