Question

A single current-carrying loop of wire carrying current I flows in the anticlockwise direction (seen from the +z direction) and lies in the xy plane. The plot of \(\hat{j}\) component of magnetic field (\(B_y\)) at a distance a (less than radius of the coil) and on the yz plane vs z coordinate looks like:

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

For magnetic field due to current loops:
• Use the right-hand rule to determine the direction of the field.
• Symmetry plays a critical role in analyzing magnetic field variations.

Answer 1

The Correct Option is A

To solve this problem, we need to determine the behavior of the \(B_y\) component of the magnetic field created by a current loop at a certain point in space.

Given:

• A current-carrying loop with current \(I\) flowing anticlockwise as viewed from the positive \(z\)-direction.
• The loop lies on the \(xy\)-plane.
• We need to analyze the \(\hat{j}\) (or \(B_y\)) component of the magnetic field at a distance \(a\) on the \(yz\)-plane.

Concepts and Analysis:

According to Ampere's Law and Biot-Savart Law, the magnetic field due to a loop of wire has cylindrical symmetry around the axis of the loop (in this case, the \(z\) axis). The magnetic field at a point off the axis can be understood as having three components \((B_x, B_y, B_z)\), but here we only consider the \(B_y\) component.

At any plane parallel to \(xy\), due to the symmetry and direction of the current, it is expected that the \(B_y\) component is non-zero. For positions symmetrically above or below the loop, the vertical component will change direction.

Specifically, the \(B_y\) component at a distance will show a sign change as the position crosses the plane of the loop (\(z=0\)).

Correct Option:

The observed behavior is graphically represented in the correct answer image:

This plot contains matching behavior for \(B_y\), which is zero at the loop center and changes sign as one moves through \(z=0\).

Reasoning Behind Incorrect Options:

• Other options would not correctly represent the field behavior across the \(z\) axis.
• The symmetry and direction of the field vary inconsistently with those presented in the incorrect images.