What is the direction of the magnetic field b⃗ a at point a?

Use the Right -hand Rule to find the direction of the magnetic field.

Explanation: A magnetic force only occur, in a magnetic field, when a particle is moving perpendicularly relative to the magnetic field. So, all three quantities are perpendicular among themselves.

The Right-Hand Rule apply for the positive charges moving in conventional current. If the moving charge is negative, the velocity must be reversed.

Right-Hand Rule determines the direction of any or all of the three and it is as follows: With you right hand, point your index finger in the direction of the velocity, your middle finger in the direction of the magnetic field and your thumb will be pointing in the direction of the magnetic force.

Another way of using the rule is when there is a current carrying wire:

The fingers of your right hand will curl into a half circle around the wire, they will point in the direction of the field. The thumb will point in the direction of the conventional current.

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