Question

A person is standing facing geographic north and a vertical wire in front of him is carrying a current in downward direction. The direction of magnetic field at a point on the right side of wire is:

• A. South
• B. East
• C. West
• D. North

Hint:

Use the right-hand thumb rule with the thumb along the downward current. The point on the right of a person facing north is east of the wire.

Answer 1

The Correct Option is A

Step 1: Choose coordinates:
Let east be the +x direction, north the +y direction and up the +z direction. The wire is along the z axis. The current flows down, so it points along $-\hat{z}$.
The person faces north, so the right side is east. The point is at $+x$ from the wire, so the position vector from the wire is $\hat{r} = +\hat{x}$.

Step 2: Use the vector form of the field law:
The field of a long straight current is along the direction of $\vec{I} \times \hat{r}$, where $\hat{r}$ points from the wire to the point.
\[ \vec{B} \parallel (-\hat{z}) \times (\hat{x}) \]

Step 3: Work out the cross product:
We know $\hat{z} \times \hat{x} = +\hat{y}$. So $(-\hat{z}) \times \hat{x} = -\hat{y}$.
The direction $-\hat{y}$ is the south direction.

Step 4: Cross-check by elimination:
The field must be perpendicular to both the wire (vertical) and the line from the wire to the point (east-west). The only directions left are north and south, so (B) and (C) cannot be right.
For an upward current the field at this point would be north. Our current is downward, so the field is reversed, and it is south, not north.

Final Answer:
The magnetic field at the point on the right of the wire is towards the south, which is option (A). \[ \boxed{\text{South}} \]