In SI units, the number of turns per unit length of a solenoid is 200 having total length 0.5m, then
total number of tums of that solenoid will be
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Number of turns on the solenoid = 15 turns/cm = 1500 turns/m
Number of turns per unit length, n = 1500 turns
The solenoid has a small loop of area, A =2.0cm
2
Current carried by the solenoid changes from 2 A to 4 A.
Change in current in the solenoid, di=4−2=2A
Change in time, dt=0.1s
Induced emf in the solenoid is given by Faraday’s law as:
e=
dt
dϕ
...(i)
Where,
ϕ= Induced flux through the small loop
=BA ... (ii)
B= Magnetic field
=μ
0
ni ...(iii)
μ0= Permeability of free space
=4π×10
−7
H/m
Hence, equation (i) reduces to:
e=
dt
d
(BA)
=Aμ
0
n×(
dt
di
)
=2×10
−4
×4π×10
−7
×1500×
0.1
2
=7.54×10
−6
V
Hence, the induced voltage in the loop is 7.54×10
−6
V.
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