Two solenoids made of insulated conducting wires and of equal lengths are such that one is wound over another. Resistance of each of them is R and number of turns per unit lenghts is n. The solenoids are now conected in series and if current flows through them in the same direction in both cases, determine the magnetic field along the axis of solenoids in each case.

Explanation

In case of series combination, equivalent resistance =2R and hence current through each solenoid, `I_(s)=(E)/(2R)`
Hence, the resultant magnetic field along the axis,
`B=B_(1)+B_(2)mu_(0)nI_(p)+mu_(0)nI_(P)`
`=2mu_(0)n*(E)/(2R)=(mu_(0)nE)/(R)`