Question

A straight long wire lying along $y$-axis, carries a current of $1\ \text{A}$ along $-y$ direction. The magnetic field due to the conductor at a point $(50\ \text{cm},\,0,\,0)$ will point along:

• A. $z$-axis
• B. $-z$-axis
• C. $x$-axis
• D. $-x$-axis

Hint:

Use the right-hand thumb rule with the thumb along the current (-y) and find the circulation direction at a point on +x.

Answer 1

The Correct Option is A

Step 1: Set up the picture:
Imagine the wire along the $y$-axis. The current runs downward, that is, toward negative $y$. The observer stands at a point on the positive $x$ side.

Step 2: Use the thumb rule with the picture:
Hold the right hand so the thumb points along $-y$. The fingers curl around the wire.
Looking from the $+y$ end down the wire, the current points away from the viewer, so the field circulates clockwise in the $xz$ plane.

Step 3: Locate the field at the point:
Take the axes with $x$ to the right and $z$ upward in the plane of view, with $y$ coming toward the viewer. Then clockwise motion means that at the right side ($+x$), the field points upward in this picture.
Check with axes: a right-handed set has $\hat{i}\times\hat{j}=\hat{k}$. With $\hat{i}$ to the right and $\hat{j}$ toward the viewer, $\hat{k}$ points up. So the field at $+x$ is along $+z$.

Step 4: Cross-check with a limiting case:
Reverse the current to $+y$. The thumb rule then gives $-z$ at the same point. Our wire has current along $-y$, so the field is opposite to that, which is $+z$.
The field can never lie along the line from wire to point, so the options with $x$ are rejected at once.

Final Answer:
The magnetic field at the point is along $+z$. The correct option is (1). \[ \boxed{z\text{-axis (option 1)}} \]