Question

A coil of mean area 500cm^2 having 1000 turns is held perpendicular to a uniform magnetic field of 0.4 G. The coil is turned through π rad. in 1/10 sec. Calculate the average induced e.m.f

Answer 1

Given, A = 500 cm² = 500 × 10⁻⁴ = 0.05 m²
Number of turns = N = 1000
Magnetic field = B = 0.4G =0.4 × 10⁻⁴T
∆t = time taken = 1/10 = 0.1 sec

Coil turned θ = 0° to θ = 180° as shown in figure.
Change in flux = $\bold{\Phi_f-\Phi_i}$
$\bold{\Phi_i=NBAcos0^{\circ}=NBA}\\\bold{\Phi_f=NBAcos180^{\circ}=-NBA}$
so, change in flux = ΔΦ = -2NBA

We know,
$\bold{E_{av}=\frac{-\Delta{\Phi}}{\Delta{t}}}$
Where Eav is average induced emf
So, Eav = 2NBA/∆t
=2 × 1000 × 0.4 × 10⁻⁴ × 0.05/0.1
=0.04 V