---
title: "A small circular wire loop of radius \\(r\\) is coplanar and concentric with a much larger circular wire loop of radius \\(R\\), where \\(r \\ll R\\). The mutual inductance of this two-loop system is \\(M_0\\). If the radius of the inner loop is changed to \\(2r\\) and the radius of the outer loop is changed to \\(2R\\), while maintaining \\(2r \\ll 2R\\), what is the new mutual inductance of the system in terms of \\(M_0\\)?"
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url: "https://nerd-notes.com/ubq/121312/"
date_modified: "2026-08-23T04:59:40+00:00"
---

# A small circular wire loop of radius \(r\) is coplanar and concentric with a much larger circular wire loop of radius \(R\), where \(r \ll R\). The mutual inductance of this two-loop system is \(M_0\). If the radius of the inner loop is changed to \(2r\) and the radius of the outer loop is changed to \(2R\), while maintaining \(2r \ll 2R\), what is the new mutual inductance of the system in terms of \(M_0\)?

A small circular wire loop of radius \(r\) is coplanar and concentric with a much larger circular wire loop of radius \(R\), where \(r \ll R\). The mutual inductance of this two-loop system is \(M_0\). If the radius of the inner loop is changed to \(2r\) and the radius of the outer loop is changed to \(2R\), while maintaining \(2r \ll 2R\), what is the new mutual inductance of the system in terms of \(M_0\)?

![A schematic diagram showing two concentric coplanar circles lying in the plane of the page. The outer circle is drawn as a thin solid circular line centered at point O. A dashed line segment extends radially from the center point O to the top edge of the outer circle, ending in an arrowhead labeled R. The inner circle is drawn as a smaller solid circular line centered at the same point O. A dashed line segment extends radially from point O toward the upper-right at 45 degrees to the inner circle, ending in an arrowhead labeled r. The radius R is significantly larger than radius r. A single small dot marks the common center point O. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461179-LldrTi.jpg)

- **A.** \(\dfrac{1}{4} M_0\)
- **B.** \(\dfrac{1}{2} M_0\)
- **C.** \(M_0\)
- **D.** \(2 M_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121312/*