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Lecture 5: Motion in Magnetic Fields and the B-Field
February 4, 2025
Reading Assignment
- Read: 26.5-26.6
- Study: Eqs 26.7, 26.15, Exs 26.3, 26.4
Objectives
- (Continuing objective) Describe applications of the concepts of electricity and magnetism to everyday “real-life” situations.
- Calculate the force (magnitude and direction) acting on moving charges and current-carrying conductors in a magnetic field.
- Starting from Newton's 2nd law, relate the velocity, magnetic field strength, and radius of curvature for a particle moving in a uniform magnetic field.
- For a current loop or coil in a uniform magnetic field, calculate the magnetic moment, the torque on the coil, and the magnetic energy.
- 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) inside and just outside the central region of a very long solenoid, (c) outside a wire segment or long straight wire. Use these and superposition to find the total B-field due to a combination of sources.
Homework
- Wednesday's Assigned Problems:
A14, A15, A110; CH 26: 27, 31, 55, 61, 63, 65
Notes: Do not use Eq. 26.11 for problem 65.
- Monday's Hand-In Problems from Lecture 5:
X5 (below), X6 (below); CH 26: 28, 32, 80
Note: this is only the first half of the hand-in set.
Problem X5 A single-turn wire loop 10 cm in diameter carries a $12\,\mbox{A}$ current. It experiences a $0.015\,\mbox{N$\cdot$m}$ torque when the normal to the loop plane makes a $25^\circ$ angle with a uniform magnetic field. Find the magnetic field strength.
Problem X6 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.
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - 6; CT2 - 3; CT3 - 7; CT4 - 5; CT5 - 2; CT6 - 6; CT7 - 3
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 torque on a coil with multiple turns
- 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
- Losing My Religion - REM
- Ain't No Mountain High Enough - Tammi Terrell & Marvin Gaye
- Cold Shot - Stevie Ray Vaughan
- The Best of What's Around - Dave Matthews Band
- Respect - Aretha Franklin
Assigned Problems Guide
- A14: quck toy kit problem, making a compass!
- A15: medium quick toy kit problem, sketching the B-field from observing the compass.
- A110: Challenging: finding B_wire from a couple of wires, thinking carefully about their directions, and then added the vectors together.
- 26-27: medium. a straightforward B_loop calculation, but you need to figure out first how many turns the loop has.
- 26-31: medium. Finding the torque on a wire loop, very similar to what we did in lecture.
- 26-55: medium-long. Use the max torque and B field to determine the magnetic moment. Then use information about the coil to find I from the magnetic moment.
- 26-61: medium-quick. Break it into separate contributions to the B-field, and once you've found them, add them back together. Think about the direction of the field.
- 26-63: medium-quick. Same advice as the last problem. The answer in Wolfson is wrong. It should be $\mu_0 I/4a$.
- 26-65: long/challenging. Divide and conquer! Current $I_1$ creates a magnetic field $B_1$. Find the forces on current $I_2$ due to the field $B_1$. Consider each segment of the rectangle separately. Then add for the net force.