r ˆ

r ˆ dl dl dB dB dB sin ϕ dB cos ϕ dB cos ϕ dB sin ϕ O x z y According to Biot-Savart’s law, the magnetic field at P due to the current element at C is dB Idl µ The magnitude of dB is dB Idl Idl µ θ µ   sin where θ is the angle between Idl  and  r . Here θ = °. The direction of dB is perpendicular to the current element Idl  and CP. It is therefore along PR perpendicular to CP. The magnitude of magnetic field at P due to current element at D is same as that for the element at C because of equal distances from the coil. But its direction is along PS. The magnetic field dB due to each current element is resolved into two components; dB cos ϕ along y-direction and dB sin ϕ along z-direction. The horizontal components cancel out while the vertical components ( dB sin ϕ k  ) alone contribute to the net magnetic field B at the point P. dB dB k