Question

L is a circular loop carrying a current. P is a point on its axis OX. dl is an element of length on the loop at a point A on it. The magnetic field at P:

(This question has multiple correct options)
(A). due to L is directed along OX
(B). due to dl is directed along OX
(C). due to dl is perpendicular to OX
(D). due to dl is perpendicular to AP

Answer 1

Hint: There is a right hand thumb rule with the help of which we can predict the direction of the magnetic field due to the circular loop carrying a current. If we curl the right-hand fingers round the coil in the direction of the current then the thumb will represent the direction of the magnetic field.

Complete step-by-step answer:
If we see the small part of the coil dl then by the right-hand thumb rule the magnetic field will be along the perpendicular to AP.
So, option (D) is also correct.
Now, if we apply the right-hand thumb rule, we find that if we curl the right-hand fingers in the direction of the current in the coil then the thumb will represent the magnetic field. Here the magnetic field will be directed towards the axis of the coil which is OX. Also, if we consider that the loop is a combination of the many small parts like dl then the vertical component will be cancelled out and the magnetic field due to the whole loop will be horizontal that is along OX.
So, the magnetic field at P due to L will be directed along OX
Hence the option (A) is correct.
Hence for the above question the option (A) and (D) are correct.

Note: The magnetic field lines are concentric circles at every point of a current carrying circular loop and the direction at each point or each section of the current carrying loop can be determined by the right-hand thumb rule as discussed earlier. The magnetic field due to the current carrying loop will be found uniform only at the centre of the current loop and non-uniform near the circular coil.