Question

Net magnetic field at the centre of the circle ‘O’ due to a current through a loop as shown in the figure is:

A. zero
B. perpendicular to paper inwards
C. perpendicular to paper outwards
D. perpendicular to the paper inwards if $\theta \le 90{}^\circ$ and perpendicular to paper outwards if $90{}^\circ \le \theta \le 180{}^\circ$

Answer 1

The question is based on the property of the magnetic field produced by a circular loop. The magnetic field lines are straight at the centre, whereas, at the axis, they are in a clockwise and anticlockwise direction, based on the direction of the current flowing through the circular loop.

Complete answer:
From the data, we have the data as follows.
The direction of the flow of the current through the circular loop is anti-clockwise.
Using a right-hand thumb rule, the direction of the magnetic field produced in a circular loop can be determined.
The magnetic field lines will be straight at the centre.
With the direction of the current being anti-clockwise, using the right-hand thumb rule, it is clear that the net magnetic field at the centre of the circle ‘O’ due to a current through a loop will perpendicular to paper outwards.
As, the direction of the net magnetic field at the centre of the circle will be perpendicular to paper outwards.

Thus, option (C) is correct.

Note:
The direction of the magnetic lines of force produced by the magnetic field will be the same at every segment of the circular loop. The flow of current is the cause for the production of the magnetic field around the circular loop. The magnetic field produced by a circular loop will be more concentrated towards the centre (inside of the loop) when compared to that outside of the loop.