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Question
A small flat search coil of area 5cm2 with 140 closely wound turns is placed between the poles of a powerful magnet producing magnetic field 0.09T and then quickly removed out of the field region. Calculate:
(a) Change of magnetic flux through the coil, and
(b) emf induced in the coil.
Solution 1
a = 5cm2
= 5 × 10-4 m2
n = 140
(a) B = 0.09T
`Φ = bar(B) . bar(A) = BA cos theta = 0.09 xx 5 xx10^(-4) xx 1`
= 0.45 × 10-4 W b
(b) `e = n (d phi )/(dt)`
= `140 xx (0.45 xx 10^(-4))/dt`
but dt is very small
dt → 0
`therefore -> ∞`
Solution 2
Number of turns in the coil, N = 140
Area of cross-section of the coil = 5 cm2
The magnetic field, B = 0.09 T
(a) Flux linked with the coil, Φ = NBA cos θ
θ = 0° , Φi = NBA
⇒ Φi = 140 × 0.09 × 5 × 10-4
⇒ Φi = 6.3 × 10-3 Weber
When the coil is quickly removed, the flux linkage becomes zero,Φf = 0
Hence change in magnetic flux through the coil,
ΔΦ = Φf -Φi = (0 - 6.3 × 10-3) Weber
ΔΦ = - 6.3 × 10-3 Weber
(b) Let the coil is removed in a very short period of time-interval, dt = 1s, then induced emf,
`"e" = -("d"phi)/("dt") = - ((-6.3xx10^-3)/1) = 6.3 xx 10^-3 "V"`
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