---
title: "A hemispherical surface of radius \\(R\\) is placed in a uniform magnetic field of magnitude \\(B\\). The field vectors are parallel to the central symmetry axis of the hemisphere and enter through its open, flat circular base. What is the magnitude of the magnetic flux through the curved surface of the hemisphere?"
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url: "https://nerd-notes.com/ubq/118639/"
date_modified: "2026-08-04T08:13:25+00:00"
---

# A hemispherical surface of radius \(R\) is placed in a uniform magnetic field of magnitude \(B\). The field vectors are parallel to the central symmetry axis of the hemisphere and enter through its open, flat circular base. What is the magnitude of the magnetic flux through the curved surface of the hemisphere?

A hemispherical surface of radius \(R\) is placed in a uniform magnetic field of magnitude \(B\). The field vectors are parallel to the central symmetry axis of the hemisphere and enter through its open, flat circular base. What is the magnitude of the magnetic flux through the curved surface of the hemisphere?

![A three-dimensional diagram showing a hemispherical shell with radius R placed with its flat circular base resting in the xy-plane centered at the origin. A curved dome extends upward into the +z region. Exactly four parallel, evenly spaced vertical magnetic field arrows, labeled \vec{B}, point straight upward in the +z direction, passing through the flat circular base and exiting through the top of the curved dome. A radius arrow labeled R extends from the origin to the circular rim of the base in the xy-plane. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831204-zs3EY4.jpg)

- **A.** \(\pi R^2 B\)
- **B.** \(2\pi R^2 B\)
- **C.** \(4\pi R^2 B\)
- **D.** \(0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118639/*