Question

Magnetic needle placed at distance r from straight conductor of length 8r carrying current I shows a deflection of Ф degree what may be the deflection on passing the same current when conductor is bent in form of square and magnetic needle is placed at point of intersection of diagonals of square. reason

Answer 1

The magnetic field or the force and hence the deflection of the magnetic needle are proportional to the length of the conductor and is inversely proportional to the square of the distance from the conductor.

case 1 :  Force = K * 8 r / r²  = 8 K / r

case 2 : Force = 4 * [ K * 2 r / r² ]  =  8 K / r , 

       Here the needle is in the center of a square, and each side is 2 r. The perpendicular distance  of the needle from each side is r, as the needle is at the center.    Force due to each side is added, as they are all in the same direction, along the tangent of a circle around the conductor, with radius = r and passing through the needle.

Hence the deflection remains same.