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Moving Charges And Magnetism

Question
CBSEENPH12040120

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 10π2 Ω, the total charge flowing through the coil during this time is

  • 32 πμC

  • 16 μC

  • 32 μC

  • 16 πμC

Solution

C.

32 μC

straight epsilon space equals space minus space straight N dϕ over dt
open vertical bar straight epsilon over straight R close vertical bar space equals space straight N over straight R dϕ over dt
dq space equals straight N over straight R space dϕ
increment straight Q space equals space fraction numerator straight N left parenthesis increment straight ϕ right parenthesis over denominator straight R end fraction
increment straight Q space equals space fraction numerator increment straight ϕ subscript total over denominator straight R end fraction
open parentheses NBA over straight R close parentheses
space equals space fraction numerator straight mu subscript 0 niπr squared over denominator straight R end fraction
Putting space values
fraction numerator 4 straight pi space straight x space 10 to the power of negative 7 end exponent space straight x space 100 space straight x 4 space xπ space straight x space left parenthesis 0.01 right parenthesis squared over denominator space 10 straight pi squared end fraction space
increment straight Q space equals space 32 μC