A long solenoid having n = 200 turns per metre has a circular cross-section of radius `a_(1) = 1 cm`. A circular conducting loop of radius `a_(2) = 4 cm` and resistance ` R = 5 (Omega)` encircles the solenoid such that the centre of circular loop coincides with the midpoint of the axial line of the solenoid and they have the same axis as shown in Fig.

A current 't' in the solenoid results in magnetic field along its axis with magnitude `B = (mu)ni` at points well inside the solenoid on its axis. We can neglect the insignificant field outside the solenoid. This results in a magnetic flux `(phi)_(B)` through the circular loop. If the current in the winding of solenoid is changed, it will also change the magnetic field `B = (mu)_(0)ni` and hence also the magnetic flux through the circular loop. Obvisouly, it will result in an induced emf or induced electric field in the circular loop and an induced current will appear in the loop. Let current in the winding of solenoid be reduced at a rate of `75 A //sec`.
Magnetic of induced electric field strength in the circular loop is nearly We know that there is magnetic flux through the circular loop because of the magnetic field of current in the solenoid. For the purpose of circular loop, let us call it the external magnetic field. As current in the solenoid is reducing, external magnetic field for the circular loop also reduced resulting in induced current in the loop. Finally, as the solenoid current becomes zero, external field for the loop also becomes zero and stop changing. However, induced current in the loop will not stop at the instant at which the external field stops changing. This is because induced current itself produces a magnetic field that results in a flux through the loop. External field becoming zero without any further change will compel the induced current in the loop to become zero and so magnetic flux through the loop due to change in induced current will also change resulting in a further induced phenomenon that sustains currents in the loop even after the external field becomes zero.

Options

A. `4.7 xx 10^(-7) Vm^(-1)`
B. `3.82 xx 10^(-6) Vm^(-1)`
C. `2.3 xx 10^(-5) Vm^(-1)`
D. None of these

Answer

C

Explanation

As found in privious part, the induced current is `i=1.18 mu A`
Thus, induced voltage is `V=iR=5.9 muA`
Thus, magnitude of induced field stramgth in the circular loop is
`E=V/(2 pi a_(2)) = 2.3 xx 10^(-5)V//m`.