A long cylindrical conductor of radius a has two cylindrical cavities of diameter a through its entire length as shown in cross-section in figure. A current `I` is directed out of the page and is uniform throughout the cross-section of the conductor. Find the magnitude and direction of the magnetic field in terms of `mu_0,I,r` and a.

(a) at point `P_1` and (b) at point `P_2`

Answer

[(a) `(mu_(0)l)/(pir)((2r^(2)-a^(2))/(4r^(2)-a^(2)))` to the left ; (b) `(mu_(0)l)/(2pi)((2r^(2)+a^(2))/(4r^(2)+a^(2)))` towards the top of the page]