(a). Find the magnetic field B at point O (centre) of
(i). ABCD, which is a square of side l.
(ii). ABC, which is an equilateral triangle of side l.


(b) Twelve uniform wires of equal length l and each of resistance r are connected to form a skelton cube. A battary of emf E is connected between two diagonally opposite corners of the cube. The magnetic induction at the centreof the cube is .........
(c) An infinately long straight wire is placed at the origin along the z-axis. The current I flows along the positive z-axis. Find the unit vecotrs showing the direction of magnetic field at the four points: `P(a,0), Q(0,b), R(a,0) and S(0,-b)`

Explanation

(a) i. Magnetic field due to the upper tow branches will
cancel out that due to lower branch and will be zero at
centre.
(ii) Magnetic field due to the upper two branches will cancel
out the magnetic field due to the lower branch.


(b) Magnetic field due to each pair of wire will cancel out. Net
magnetic field will be zero.
(c)