Question

On connecting a battery to the two corners of a diagonal of a square conductor frame of side at the magnitude of the magnetic field at the center will be:
A. zero
B. $\dfrac{{{\mu _0}}}{{\pi a}}$​​
C. $\dfrac{{2{\mu _0}}}{{\pi a}}$
D. $\dfrac{{4{\mu _0}i}}{{\pi a}}$

Answer 1

In order to solve this type of theory question we need to draw a convenient diagram which consists of the diagonal square conductor frame connected to a battery such that the magnetic field produced. From the reference of the direction of the magnetic field we can find the solution.

Complete step by step answer:

The above diagram is constructed such that the diagonal square conductor frame is connected to a battery which produces the magnetic field in a different direction with respect to the components of the frame. In the diagram a symbol cross indicates the magnetic field is passing into the frame or page, as though it flows away from us. A symbol dot indicates that the magnetic field is flowing out of the frame or page, as though it is coming toward us.
Hence we take the reference of above diagram the magnetic field is flowing in the frame AB and BC is showing inward direction and magnetic field is flowing in the frame CD and DA is showing outward direction. Therefore the net magnetic field at the center of the square of the frame is taken as zero or the magnetic field due to AB, BC, CD and DA components of the frame flowing in and out which is the same at the center of the square of the frame.
The correct option is A.

Note: Here we consider four sides of a square frame as four separate current carrying wires. When we apply Fleming's left hand rule to find the force on each side. Forces on each side that is (top, bottom, left and right) carries equal and opposite direction therefore net force on the square loop is taken as zero