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Lecture 6: Magnetic Fields
February 5, 2026
Reading Assignment
- Read: 26.5, “Solenoids” in 26.8
- Study: Eqs 26.7, 26.15, 26.21; Fig 26.21; Exs 26.3, 26.4, 26.9
Objectives
- (Continuing objective) Describe applications of the concepts of electricity and magnetism to everyday “real-life” situations.
- Correctly sketch the direction of the magnetic field in the vicinity of variously shaped magnets, especially near the North or South poles.
- Use the Biot-Savart law and the right-hand rule to determine the magnitude and direction of a magnetic field due to a short current segment.
- Distinguish and correctly use the expressions for the magnetic field for each of these special situations: (a) at the center of a circular loop or finite arcs of a circular loop; (b) a very long solenoid, (c) a long straight wire. Use these and superposition to find the total B-field due to a combination of sources.
Homework
- Friday's Assigned Problems:
A21, A22, A15, A110, X6 (below); CH 26 27, 61, 63, 65
Problem X6 A solenoid used in a plasma physics experiment is 10 cm in diameter, is 1.0 m long, and carries a 35 A current to produce a 100 mT magnetic field. (a) How many turns are in the solenoid? (b) If the solenoid resistance is $2.7\,\Omega$, how much power does it dissipate?
Answers: X6 (a) 2300, (b) $3.3\,\text{kW}$
Notes: For CH 26 #65 do not use Eq. 26.11. For CH 26 #63 the answer in the back of Wolfson is incorrect. It should be $\mu_0 I/4a$.
- Monday's Hand-In Problems:
X7 (below); CH 26 28, 68, 70, 80
Note: This is only the second half of the hand-in set.
Problem X7 Three parallel wires of length $\ell$ each carry current $I$ in the same direction. They're positioned at the vertices of an equilateral triangle of side $a$, and oriented perpendicular to the triangle. Find an expression for the magnitude of the force on each wire. Hint: sketch the end-on view so 3 wires are shown as dots in an equilateral triangle, each carrying current out of the page. First find ${\vec B}$ at the top wire due to currents in the other two wires. You can treat the wires as infinitely long to find the field. Then find the force.
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - back; CT2 - 5; CT3 - 2; CT4 - 6; CT5 - 3
- Right Hand Rules in Magnetism
Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.- Example of determining the direction of $\vec{B}$ using the curly-straight RHR
- Example of determining the direction of $\vec{B}$ using $d\vec{l} \times \vec{r}$
- Example of determining $\vec{B}$ for a long, straight wire
- Determining the total magnetic field from two wires. NOTE: near the end, we accidentally leave out a negative sign in the x-components, but we catch that error and fix it at the very end of the video.
Pre-Class Entertainment
- It's Too Late - Carole King
- Me and Julio Down by the Schoolyard - Paul Simon
- Better Together - Jack Johnson
- Eet - Regina Spektor
- Subterranean Homesick Blues - Bob Dylan