Q 1 :    

A long solenoid of diameter 0.1 m has 2×104 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10π2Ω, the total charge flowing through the coil during this time is               [2017]
 

  • 16 μC

     

  • 32 μC

     

  • 16π μC

     

  • 32π μC

     

(2)

Given, n=2×104, I=4 A

Initially I=0 A                Bi=0 or ϕi=0

Finally, the magnetic field at the centre of the solenoid is given as

           Bf=μ0nI=4π×10-7×2×104×4=32π×10-3 T

Final magnetic flux through the coil is given as

         ϕf=NBA=100×32π×10-3×π×(0.01)2

         ϕf=32π2×10-5Tm2

Induced charge, q=|Δϕ|R=|ϕf-ϕi|R=32π2×10-510π2

           =32×10-6C=32 μC