A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2placed inside the solenoid normal to its axis. If the current carriedby the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what isthe induced emf in the loop while the current is changing?
Given: The number of turns in solenoid per centimeter is 15 , the area of the loop is 2.0 cm 2 and the current changes from 2 A to 4 A in 0.1 s .
The number of turns per meter is,
n = 15 × 100 = 1500
The induced flux is given as,
ϕ = B A = μ 0 n i A
Where, μ 0 is the permeability of free space, i is the current and A is the area.
According to Faraday’s law, the induced emf in a solenoid is given as,
e = d ϕ d t = d d t ( μ 0 n i A ) = A μ 0 n d i d t
Where, ϕ is the induced flux and t is time.
By substituting the values in the above equation, we get
e = 2 × 10 − 4 × 4 π × 10 − 7 × 1500 × ( 4 − 2 ) 0.1 = 240000 × 3.14 × 10 10 = 7.54 × 10 − 6 V
Thus, the induced emf in the loop is 7.54 × 10 − 6 V .
Given: The number of turns in solenoid per centimeter is
The number of turns per meter is,
The induced flux is given as,
Where,
According to Faraday’s law, the induced emf in a solenoid is given as,
Where,
By substituting the values in the above equation, we get
Thus, the induced emf in the loop is
