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.

Answer 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 -> ∞` 

Answer 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° , Φ_i = NBA

⇒ Φ_i  = 140 × 0.09 × 5 × 10^-4

⇒ Φ_i = 6.3 × 10^-3 Weber

When the coil is quickly removed, the flux linkage becomes zero,Φ_f = 0

Hence change in magnetic flux through the coil, 

ΔΦ = Φ_f -Φ_i = (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"`