phy-e.m.f.

The solenoid is of finite length (50 cm) and hence formula for infinitely long solenoid cannot be used here.

(a) The magnetic flux density B at the centre of the solenoid is given by
B = (4.pi x 10^-7) x (1000/0.5) x 5 x [0.25/0.262] T = 0.012 T

Flux linkage with the wire = 5 x 0.012 x 0.02 T = 1.2 x 10-3 wb

(b) Induced emf = rate of change of magnetic flux
hence, induced emf = 1.2x10^-3/0.05 v = 0.02 v

a. Total flux linkage = nBA

For solenoid, B = u0NI

So, flux linkage of the wire = nu0NIA = (5)(4pi X 10^-7)(1000)(5.0)(0.020)

= 6.28 X 10^-4 Tm^2


b. By induced e.m.f. = -nd(BA)/dt = -nu0NA dI/dt

= -(5)(4pi X 10^-7)(1000)(0.020)(0 - 5.0)/(0.050)

= 1.26 X 10^-2 V