Final answer:
The maximum electric field strength at a point 1.4 cm from the solenoid axis can be estimated using Faraday's law, but precise calculation cannot be performed without additional information on the rate of change of magnetic flux. The value of B when E is at its maximum is the mean of the sinusoidal variation, which is 10.0 T.
Step-by-step explanation:
To determine the maximum electric field strength at a point 1.4 cm from the solenoid axis when the magnetic field inside a solenoid varies sinusoidally, Faraday's law of electromagnetic induction is applied. According to this law, a changing magnetic field will induce an electric field. While the exact calculation of such an electric field may require advanced knowledge of Maxwell's equations and boundary conditions, typically it can be approximated using the formula:
E = αBr
where E is the induced electric field, α is the rate of change of the magnetic flux (α = dB/dt), B is the magnetic field strength, and r is the radial distance from the axis of the solenoid. However, since this problem doesn't provide the rate of change of the magnetic field directly, a calculation assuming ideal conditions would not be possible without additional information or assumptions.
Regarding the second part of the question, the value of B at the instant E reaches its maximum value can be understood conceptually. The electric field induced in the region surrounding the solenoid is directly related to the rate of change of the magnetic field, according to Faraday's law. The electric field strength is maximal when the rate of change of the magnetic field is maximal. For a sinusoidal change in magnetic field, this occurs when the magnetic field is at the mean value as it transitions between the minimum and maximum, which in this case is (8.0 T + 12.0 T) / 2 = 10.0 T.