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title: "A large, thin conducting sheet located in the horizontal plane carries a uniform surface current per unit width \\(K_0\\). Directly above the sheet, the magnetic field is uniform with magnitude \\(B_1 = \\dfrac{\\mu_0 K_0}{2}\\) pointing parallel to the sheet. Directly below the sheet, the magnetic field has the same magnitude \\(B_2 = \\dfrac{\\mu_0 K_0}{2}\\) but points in the opposite horizontal direction. Which of the following best explains why the tangential component of the magnetic field undergoes a step discontinuity across the surface of the sheet?"
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url: "https://nerd-notes.com/ubq/118582/"
date_modified: "2026-08-04T08:11:27+00:00"
---

# A large, thin conducting sheet located in the horizontal plane carries a uniform surface current per unit width \(K_0\). Directly above the sheet, the magnetic field is uniform with magnitude \(B_1 = \dfrac{\mu_0 K_0}{2}\) pointing parallel to the sheet. Directly below the sheet, the magnetic field has the same magnitude \(B_2 = \dfrac{\mu_0 K_0}{2}\) but points in the opposite horizontal direction. Which of the following best explains why the tangential component of the magnetic field undergoes a step discontinuity across the surface of the sheet?

A large, thin conducting sheet located in the horizontal plane carries a uniform surface current per unit width \(K_0\). Directly above the sheet, the magnetic field is uniform with magnitude \(B_1 = \dfrac{\mu_0 K_0}{2}\) pointing parallel to the sheet. Directly below the sheet, the magnetic field has the same magnitude \(B_2 = \dfrac{\mu_0 K_0}{2}\) but points in the opposite horizontal direction. Which of the following best explains why the tangential component of the magnetic field undergoes a step discontinuity across the surface of the sheet?

![A thin horizontal plane representing a surface current sheet lies in the xy-plane. A series of parallel arrows on the plane point along the positive x-axis, labeled K_0. A rectangular Amperian loop of height h and length l stands vertically, passing through the current sheet so that its top segment of length l is parallel to the sheet at height z > 0, and its bottom segment of length l is parallel to the sheet at depth z < 0. The vertical side segments of height h cross the sheet. Above the sheet, a horizontal field arrow points along the negative y-axis, labeled B_1. Below the sheet, a horizontal field arrow points along the positive y-axis, labeled B_2. The loop is oriented counterclockwise, with arrows on its segments indicating integration path direction. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831087-95cWfL.jpg)

- **A.** The magnetic field is discontinuous because magnetic field lines originate and terminate on moving electric charges, producing a non-zero magnetic charge density at the sheet surface.
- **B.** The magnetic field is discontinuous because the magnetic force on a moving charge approaches infinity directly at the boundary, requiring the field magnitude to jump abruptly to conserve energy.
- **C.** The magnetic field is discontinuous because a rectangular Amperian loop straddling the boundary encloses a finite current \(I_{\text{enc}} = K_0 \ell\), requiring the line integral \(\oint \vec{B} \cdot d\vec{\ell}\) to be non-zero and forcing a step change in the tangential component of \(\vec{B}\).
- **D.** The magnetic field is discontinuous because current elements on the left side of the sheet destructively interfere with current elements on the right side, completely canceling the magnetic field at the interface.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118582/*