A long straight wire carries current from south to north. Using the right-hand thumb rule, the magnetic field directly to the east of the wire points:

Correct Option

The correct option is Downwards

Explanation

The direction of the magnetic field produced by a current-carrying conductor is determined by the Right-Hand (or Maxwell’s Corkscrew Rule). According to this rule, if a current-carrying straight conductor is held in the right hand such that the thumb points in the direction of the current, then the curled fingers indicate the direction of the magnetic field lines surrounding the wire.

Analysis

To determine the specific direction in this scenario:

• Current Direction: The current flows from South to North. Assume the wire lies horizontally in the North-South plane.
• Application of Rule: Point the thumb of the right hand towards the North.
• Field Direction: The fingers curl around the wire.
  • On the West side of the wire, the fingers curl upwards (out of the plane).
  • On the East side of the wire, the fingers curl downwards (into the plane).

Alternatively, using the vector cross product rule ($\vec{B} \propto \vec{I} \times \vec{r}$):

• Direction of Current ($\vec{I}$): North ($\hat{j}$)
• Direction of Point ($\vec{r}$): East ($\hat{i}$)
• Cross Product ($\hat{j} \times \hat{i}$): $-\hat{k}$ (Downwards)

Thus, at a point directly to the east of the wire, the magnetic field points downwards.

Key Takeaway: The magnetic field lines around a straight current-carrying wire form concentric circles. The direction at any specific point is tangential to the circle, determined by the cross product of the current vector and the position vector.