Question

a current is flowing in a vertical wire in downward direction the direction of magnetic field of a point which is just right side to the wire is
a)towards north
b)towards south
c)towards east
d)towards west
explain the answer.....

Answer 1

Apply thumb rule
According to place you palm on current carrying conductor and surrounds the conductor with your fingers and your thumb should be in the direction of current flowing
Now at any point magnetic field lines direction will be same as direction of your finger tips

Answer 2

According to the Right hand palm rule.
" Putting the thumb of right hand in the direction of flow of current and stretching the fingers towards the point of observation, then the opening of the palm shows the direction of magnetic field at that point. "

The current is in the downward direction. So the thumb points downwards.
The point is on the right (here point P). So on opening the palm and pointing the fingers in the direction of point P, the palm faces South direction.
So option (b) is correct.