The current in an ideal, long solenoid is varies at a uniform rate of `0.01 As^(-1)`. The solenoid has 2000 turns/m and its radius 6.0 cm. (a) Consider a circle of radius 1.0 cm inside the solenoid with its axis coinciding with the axis of the solenoid. write the change in the magnetic flux through this circle in 2.0 seconds. (b) find the electric field induced at a point on the circumference of hte circle. (c) find the electric field induced at a piont outside the solenoid at a distance 8.0cm from its axis.

Explanation

Solenoid: `n=2000//m`
`(di)/(dt)=0.01A//sec` implies `di=0.01dt`
(a) Magnetic field due to solenoid
`B=mu_(0)ni`
Flux through circle of radius `r`
`phi=Bpir^(2)=mu_(o)nipinipir^(2)`
`dphi=mu_(0)npir^(2)i`
`=munpir^(2)(0.01)dt`
`phimu_(0)npir^(2)(0.01)int_(0)^(2)dt`
`=4pixx10^(-7)xx2000xxpi(0.1)^(2)(0.01)xx2`
`=4pi^(2)xx400010^(-13)=16xx10^(-9)` weber
(b) `ointvec(E).vec(dt)=(dphi)/(dt)`
`E.2pir=mu_(0)npir^(2)(di)/(dt)`
`E=(mu_(0)nr)/(2)(di)/(dt)`
`=(4pixx10^(-7)xx200xx0.1)/(2)xx0.1`
`=4pixx10^(-8)V//m`
`ointvec(E).vec(dt)=(d)/(dt)(munipiR^(2))`
`E=(munR^(2))/(2r)(di)/(dt)`
`=(4pixx10^(-7)xx2000xx(0.6)^(2)xx0.01)/(2xx0.08)`
`=18pixx10^(-8)N//m`