If 'P' is the middle point on the axis of a solenoid then derive the expression for magnetic field at that point.

Explanation

`" "costheta=(l/2)/sqrt(r^(2)+l^(2)/4)" "(##SPH_ABT_PHY_QB_XII_C04_E03_001_S01.png" width="80%">
i.e., `" "costheta=l/2 times 2/sqrt(4r^(2)+l^(2))=l/sqrt(4r^(2)+l^(2))`
here `" "B_(p)=(mu_(0)/(4pi))((2pini)/l)(2costheta)`
i.e., `" "B_(p)=mu_(0)Ni(l/sqrt(4r^(2)+l^(2)))=(mu_(0)Nil)/sqrt(4r^(2)+l^(2)) " where " N=n/l`
`therefore " "B_(p)=(mu_(0)ni)/sqrt(4r^(2)+l^(2))`