139. A long solenoid of diameter 0.1 m has 2 × 10⁴ turnsper meter. At the centre of the solenoid, a coil of 100turns and radius 0.01 m is placed with its axiscoinciding with the solenoid axis. The current in thesolenoid reduces at a constant rate to 0 A from 4 Ain 0.05 s. If the resistance of the coil is 10π²Ω, thetotal charge flowing through the coil during this time
is
(1) 32μC (2) 16 μC
(3) 32 μC (4) 16μC
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PHYSICS
A long solenoid of diameter 0.1 m has 2×10
4
turns per metre. At the center of the solenoid, a 100-turn coil of radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid is decreased at a constant rate from +2 A to - 2 A in 0.05 s. Find the total charge (in μC) flowing through the coil during this time when the resistance of the coil is 40π
2
Ω.
December 20, 2019avatar
Shravan Bindal
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ANSWER
Field at center of solenoid = B=μ
0
N
l
i where, N
l
-number of turns per unit length
Flux through the inner loop = 100×π0.01
2
B=100×π0.01
2
×μ
0
N
l
i
emf induced = rate of change of flux =
△t
△ϕ
=100×π0.01
2
×μ
0
N
l
△t
△i
Current through loop = i=
R
emf
=
△t
△ϕ
=100×π0.01
2
×μ
0
N
l
△t
△i
R
1
Total charge through the coil during this time=i△t=
△t
△ϕ
=100×π0.01
2
×μ
0
N
l
△i
R
1
=7.89×10
−5
C