What is the direction of the magnetic field at the location of the charge due to the current-carrying wire

please find the answer in the explanation.

Explanation:

The direction of the magnetic field at the location of the charge due to the current-carrying wire can be determined by using right hand rule.

The thumb points in the direction of current while the fingers curl around in the direction of the magnetic field.

The right hand rule applies to a current in a straight wire. The thumb is pointed in the direction of the current and the fingers then give the direction of the magnetic field lines.

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