Answer:
The value is [tex]\epsilon = 3.84 *10^{-5} \ V[/tex]
Explanation:
From the question we are told that
The diameter of the ring is [tex]d = 18 \ mm = 0.018 \ m[/tex]
The length of the solenoid is [tex]l = 25 \ cm = 0.25 \ m[/tex]
The diameter of the solenoid is [tex]D = 5.0 \ cm = 0.05 \ m[/tex]
The number of turns is N = 1500
The change in current in the solenoid is [tex]\Delta I = 20 \ A[/tex]
The time taken is [tex]\Delta t = 1 \ s[/tex]
Generally the radius of the ring is
[tex]r = \frac{d}{2}[/tex]
=> [tex]r = \frac{0.018 }{2}[/tex]
=> [tex]r = 0.009 \ m[/tex]
Generally the area of the ring is mathematically represented as
[tex]A = \pi r^2[/tex]
=> [tex]A = 3.142 * 0.009^2[/tex]
=> [tex]A = 2.545 *10^{-4}\ m^2[/tex]
Generally the induced emf is mathematically represented as
[tex]\epsilon = A * \frac{dB}{dt}[/tex]
Here
[tex]\frac{dB }{dt} = \mu_o * \frac{N}{l} *\frac{ \Delta I }{\Delta t}[/tex]
Here [tex]\mu_o[/tex] is the permeability of free space with value
[tex]\mu_o = 4\pi *10^{-7} \ N/A^2[/tex]
So
[tex]\frac{dB }{dt} = 4\pi * 10^{-7} * \frac{1500}{0.25} *\frac{20 }{1}[/tex]
=> [tex]\frac{dB }{dt} = 0.150816\ T/s[/tex]
So
[tex]\epsilon = 0.150816 * 2.545 *10^{-4}[/tex]
=> [tex]\epsilon = 3.84 *10^{-5} \ V[/tex]
