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: Understanding the Concept:
A long straight current-carrying wire produces a magnetic field that circles around the wire. Its direction at any point follows the right-hand thumb rule.

Step 2: Key Formula or Approach:
Point the right thumb along the current. The curled fingers then show the direction of \( \vec{B} \) around the wire. In vector form, the direction of \( \vec{B} \) is that of \( \vec{I} \times \hat{r} \), where \( \hat{r} \) points from the wire to the field point.

Step 3: Detailed Explanation:
The current flows along \( -y \), so the current direction is \( -\hat{j} \).
The point \( (50\ \text{cm}, 0, 0) \) lies on the \( +x \) axis, so \( \hat{r} = +\hat{i} \).
\[ -\hat{j} \times \hat{i} = -(\hat{j} \times \hat{i}) = -(-\hat{k}) = +\hat{k} \]
So the field at the point is along \( +z \).

Step 4: Why the other options are wrong.
Option (2), \( -z \): this is the field direction if the current were along \( +y \). The current is along \( -y \), so (2) is wrong.
Options (3) and (4), \( \pm x \): the field of a straight wire is always perpendicular to the line joining the wire and the point. That line is along \( x \), so a field along \( x \) is impossible.

Final Answer:
The magnetic field points along the \( +z \) axis, which is option (1). \[ \boxed{+z\text{-axis}} \]