A closed conducting coil of resistance 10 is placed in a magnetic field. The magnetic flux linked with the coil varies with time t as = 3t^2 + 2t + 1 Wb . The magnitude of the total charge that flows through the coil during the time interval from t = 0 to t = 2 s is:

Step-by-step solution

The total charge q that flows through a coil of resistance R due to a change in magnetic flux is given by: q = | | R First, calculate the magnetic flux at the initial and final times: At t = 0 , ₁ = 3(0)^2 + 2(0) + 1 = 1 Wb At t = 2 s , ₂ = 3(2)^2 + 2(2) + 1 = 12 + 4 + 1 = 17 Wb The change in magnetic flux is: | | = |17 - 1| = 16 Wb The total charge flown is: q = 16 10 = 1.6 C Using the instantaneous emf at t = 2 s or forgetting to divide by the resistance leads to incorrect values. Answer: 1.6 C