A long thin-walled cylindrical pipe of radius R carries total current I uniformly over its circumference. Find the magnetic field at the centre due to one quarter of the cylindrical surface shown.

Question

G1 Physics · Accepted Answer

Divide the quarter surface into parallel line-current elements. Uniform current per angular interval is dI=I dφ/(2π). Each element contributes μ₀dI/(2πR); integrating the vector directions over a quarter circle gives resultant μ₀I√2/(4π²R). Hence A.