Homework Ch 22 Cancelling Earths Magnetic Field with Two Co…

• Solve the problem above by carefully following the instructions below.

Learning Objectives

• Resolve a magnetic-field vector into horizontal and vertical components.
• Use superposition: Btotal = B1 + B2 + BE.
• Use the magnetic field at the center of an N-turn circular coil: B = 0 N I / (2R).
• Determine current directions using the right-hand rule based on the required field direction.
• Present a clear, organized solution with correct notation, units, and significant figures.

Notes: Convert Earths field into components: BEx = BEcos(61) (north), and BEy = BEsin(61) (up). To cancel Earths field, the coils must produce equal-magnitude components in the opposite directions.

Grading Details (5 pts total)

The following steps must be shown. Missing them will mean missing points.

1. Vector Diagram

• Draw the coordinate system: +x = North, +y = Up, origin at the center.
• Draw and label B1, B2, BE for the respective vectors that all start at the origin.
• B1 (field from coil 1)
• B2 (field from coil 2)
• BE (Earths field, tilted 61 above +x)
• Since the total field cancels, draw the vectors with relative sizes that clearly show B1 + B2 + BE = 0 (like a free-body diagram, but with B-vectors).
• Diagram requirement (very important): Do not redraw the coils. Instead, draw a clean vector-diagram at the center using a coordinate system where +x is North and +y is Up. At the origin, draw three magnetic-field vectors that all start at the origin and are labeled. Include the 61 angle on your diagram.

1. General Formulae (Before Numbers)

• Write the coil-center field formula: B = 0 N I / (2R).
• Write superposition in vector form: B1 + B2 + BE = 0.
• Write component equations: ?Bx = 0 and ?By = 0.
• Clearly show that x component if each vector adds to 0, and do the same with y components.

1. Symbolic Solve

• Substitute the known and unknown quantities in symbolic form to the component formulas from the previous step.
• Solve symbolically for currents: I1 and I2.

1. Substitution and Mathematical Steps

• Substitute the known values into the formulas you generated from the previous step.
• Show intermediate steps (components first, then currents).
• Include units throughout and keep the work neat.

1. Final Answer + Clarity

• No credit will be given for this step if steps 14 are skipped.
• Box or highlight the final answers with correct units and appropriate significant figures.

Submission Guidelines

• Follow the page requirements (writing, color rules, single PDF, clarity, upload method).
• Your submission must show the complete solution to this problem only. Ensure the uploaded file clearly displays the entire solution, with no steps cut off by page margins or poor image quality. Do not include unrelated material such as lecture notes, solutions to other assignments, or any extra work outside of this problem.
• After you submit: Open Submission Details View Feedback to confirm the PDF is upright, readable, and properly framed. If not, re-submit before the due time. If resubmission is after the due dateeven if the initial submission was before itthe assignment will be considered late. I always grade the latest submission and ignore earlier ones.

Late Policy

• On-time: Submit by the Due Date No penalty.
• Grace period: Between the Due Date and Available Until 10% deduction.
• After Available Until: Assignment locks; no submissions accepted Score will be 0.
• Grading: Homework is manually graded. Canvas may show 0 points until grading is complete; youll receive a notification when finished.

Submission Quality Deductions (applied to total score)

• Orientation/Legibility issues (rotated, upside down, too small/large, or blurry): 0.5 point each
• Too small handwriting (to the point that makes it hard to read and/or requires the reader to zoom in): 0.5 point
• Files added in comments or email (must be one PDF via the assignment upload only): 1 point (still must be before due date)
• Color policy violations (e.g., red/pink used for work): 0.5 point
• Did not verify submission (obviously unviewable PDF that a quick check would have caught): 0.5 point
• Repeat Issues: If the same submission problems (e.g., orientation, file format, color policy, or verification issues) occur in future assignments, the deduction will increase by an additional 0.5 points for each repeated violation.
• Unreadable or can’t be reviewed: If your submission is completely unreadable or cannot reasonably be reviewed, the entire assignment may receive a score of 0.

All work and diagrams must be your own handwriting. Typed or copied solutions may be dismissed.