A long solenoid with 20 turns per has a small loop of area 2Cm2 placed inside the solenoid normal to its axis. If the circuit carried by the solenorid changes steaditly from 1Ato 3A in 0.2s. What is the induced emf in the loop while the current ins charging.

Explanation

Give : No. of turns of long solenoid = 20 = N
No. of turns of small loop `N_(2)=1`
Length `l=1=1cm-10^(-2)m^(2)`
To find :
Iduced emf e = ?
`e=mu(dI)/(dt)`
Formula :
Mahial inductance of solenoid
`mu=(mu_(0)N_(1)N_(2)A_(2))/(l)`
`mu=(4pixx10^(-7)xx20xx10^(-4)xx2xx1)/(10^(-2))`
`=160pixx10^(-9)H`
Induced emf in the loop `e_(z).`
`e_(2)=mu.(dI)/(dt)`
`=160pixx10^(-9)xx((3-1))/(0.2)`
`=160pixx10^(-8)`
`=160xx3.14xx10^(-8)`
`=502xx10^(-8)=5.02xx10^(-6)V`\