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title: "A large, flat circular coil with \\(N_1\\) turns and radius \\(R\\) lies in a plane. A much smaller, flat circular coil with \\(N_2\\) turns and radius \\(r\\) (where \\(r \\ll R\\)) is placed at the center of the large coil and is coplanar with it. In terms of \\(N_1\\), \\(N_2\\), \\(R\\), \\(r\\), and fundamental constants, which of the following expressions represents the mutual inductance \\(M\\) of the two-coil system?"
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url: "https://nerd-notes.com/ubq/118683/"
date_modified: "2026-08-04T08:13:45+00:00"
---

# A large, flat circular coil with \(N_1\) turns and radius \(R\) lies in a plane. A much smaller, flat circular coil with \(N_2\) turns and radius \(r\) (where \(r \ll R\)) is placed at the center of the large coil and is coplanar with it. In terms of \(N_1\), \(N_2\), \(R\), \(r\), and fundamental constants, which of the following expressions represents the mutual inductance \(M\) of the two-coil system?

A large, flat circular coil with \(N_1\) turns and radius \(R\) lies in a plane. A much smaller, flat circular coil with \(N_2\) turns and radius \(r\) (where \(r \ll R\)) is placed at the center of the large coil and is coplanar with it. In terms of \(N_1\), \(N_2\), \(R\), \(r\), and fundamental constants, which of the following expressions represents the mutual inductance \(M\) of the two-coil system?

![A schematic diagram showing two concentric circular coils lying in the same horizontal plane. The outer circular coil has a large radius labeled R and is drawn with a solid line. The inner circular coil has a much smaller radius labeled r and is located at the exact center of the outer coil, drawn with a dashed line. A central dot marks the shared center point. An arrow labeled R extends from the center to the outer coil, and an arrow labeled r extends from the center to the inner coil. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831225-cZo3Nb.jpg)

- **A.** \(\dfrac{\mu_0 \pi N_1 N_2 r}{2}\)
- **B.** \(\dfrac{\mu_0 \pi N_1 N_2 R^2}{2r}\)
- **C.** \(\dfrac{\mu_0 \pi N_1 N_2 r^2}{2R}\)
- **D.** \(\dfrac{\mu_0 \pi N_1 N_2 r^3}{2R^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118683/*