Question

A magnetic compass needle is placed in the plane of paper near point $A$. In which plane should a straight current-carrying conductor be placed so that it passes through $A$ and there is no change in the deflection of the compass? Under what condition is the deflection maximum and why?

Answer 1

Explanation

1. The direction of current is perpendicular to the direction of the magnetic field, according to the right-hand thumb rule.
2. This rule will be applied to determine the magnetic needle's deflection.
3. Therefore, the magnetic field and current will meet the right-hand thumb rule if we place the current-carrying conductor in the plane of paper where the needle is situated.
4. There won't be any deviation of the needle as a result.
5. Observe the diagram:
6. 
7. According to the justification provided, positioning the current-carrying conductor in the magnetic field's plane will prevent the needle from deflecting.
8. It is obvious that when the current carrying conductor is closest to the magnetic compass, the needle's deflection will be at its greatest.

Hence, the current carrying conductor needs to be placed in the same plane as that of the paper, for the magnetic compass to attain no deflection.

Note: The right-hand thumb rule suggests that the direction of the magnetic field can be determined by wrapping our fingers around the current-carrying wire in a particular way. The direction of the current in the conductor will then be shown by the extended thumb. The right-hand thumb rule can only be used to indicate the direction of either the current or the magnetic field; it cannot be used to indicate the direction of the magnetic field.