A very long, straight solenoid with a cross-sectional area of 2.22 cm2 is wound with 85.6 turns of wire per centimeter. Starting at t = 0, the current in the solenoid is increasing according to i(t)=(0.177A/s2)t2. A secondary winding of 5.0 turns encircles the solenoid at its center, such that the secondary winding has the same cross-sectional area as the solenoid. What is the magnitude of the emf induced in the secondary winding at the instant that the current in the solenoid is 3.2A?

The induce emf is  

Explanation:

From the question we are told that

   The cross-sectional area is  

   The number of turn is

   The starting time is   = 0 s

    The current increase is  

    The number of turn of secondary winding is  

     The current at the solenoid is  

at

=>      

Generally Faraday's law of induction is mathematically represented as

substituting values

answer: option c. i.e. electric current flowing “downhill” from the negative electrode to the positive electrode in a battery

explanation:

the water analogy to the circuits define the pipes (water flows) to the electric current. now, we know that the electric current flows from the positive terminal to the circuit (as shown in the diagram attached).

hence, option c is the correct answer.

magnitude and direction