part a:
when inductor is saturated, it will behave as a short circuit.
so total impedance in the circuit=resistance of the coil=R
hence current=emf/resistance=E/R
part b:
using right hand thumb rule, it can be seen that magnetic field is in clockwise direction.
part c:
ampere's law states that if B is magnetic field,
then
integration of (B/mu)*dl=total current enclosed
==>(B/mu)*2*pi*r=N*I
==>B=mu*N*I/(2*pi*r)
part d:
energy stored=0.5*L*I^2
where L is inductance of the coil
L is directly proportional to A/r where A is cross sectional area and r is radius of the toroid.
if the toroid is shortned to half, r becomes half and A remains unchanged
so L is doubled.
as resistance is directly proportional to length/area
and length becomes half so resistance will be halved.
then current will be doubled.
the energy stored will be 2*2^2=8 times
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