AP Unit 12 Problems
11 learning problems for Unit 12. Draw the situation, name the model and explain why each step follows. These are authored practice, with worked solutions on a separate page.
Choose your next practice
Find the problems you need.
Mix the choices to focus your practice. Problem numbers and worked-solution links stay the same.
11 of 11 problems shown.
Selection: All topics and practice types.
Printing includes the currently visible selection. Reset filters first to print all 11 problems.
Problem 1
Two identical bar magnets lie on a table, both labeled N at the left and S at the right. A student proposes cutting one into two isolated poles.
Part a
Draw or describe a full field loop for one magnet and show a compass direction at two points on its principal axis, immediately outside its left and right ends.
Part b
Explain the poles produced by cutting, the interaction of two facing N ends, and how field strength changes when the probe is moved farther from a fixed magnet.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Problem 2
A class tests three small samples in the same external field. A retains strong magnetization, B has a weak temporary parallel response, and C has a weak temporary opposite response.
Part a
Identify each behavior and explain it in terms of electron-associated dipoles and domain or dipole alignment. Give one appropriate example material for A and B.
Part b
Explain what permeability measures. Why should a measurement on A specify temperature, field strength, and orientation? Contrast it with μ₀.
Part c
A compass is taken far from these samples and current sources. State an approximate model for the field that still aligns it and explain the polarity near geographic north.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Problem 3
A small positive charged object travels right at constant speed. Consider observation points U directly above it, D directly below it, and F directly ahead, all at the same distance.
Part a
Represent the magnetic field direction at U, D, and F. Explain which points have the largest field magnitude for this speed and distance.
Part b
At U, predict the change if speed increases while distance stays fixed; if distance increases while speed stays fixed; and if charge changes sign with the same magnitude.
Part c
A second positive charged object is moving right through point U. Using the first object’s source field from part (a), predict the second object’s magnetic-force direction. Distinguish the source from the responding charge, and compare the magnetic force if the second object were stationary.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Problem 4
An electron (q = −1.60 × 10⁻¹⁹ C, m = 9.11 × 10⁻³¹ kg) moves right at 1.00 × 10⁶ m/s into a 0.0200 T uniform field pointing into the page.
Part a
Derive the circular-path radius from magnetic force and centripetal force, then find the initial force and numerical radius. State what happens to speed while only B acts.
Part b
Find the direction and magnitude of an electric field that makes the electron travel straight at this speed. Explain why matching magnitudes without directions is insufficient.
Part c
If instead the velocity were parallel, antiparallel, or oblique to B, compare force magnitudes qualitatively with the original case.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Problem 5
A long straight wire runs vertically in the page and carries 5.00 A upward. A point P is 0.0400 m to its right.
Part a
Find the field magnitude and direction at P. Describe its circular geometry and components.
Part b
At fixed I = 5.00 A, create quantitative graphs of B against r and B against 1/r using points at r = 0.0200, 0.0400, and 0.0800 m. Label axes with units, use suitable scales, and plot all three points. Give the straight-line slope and predict B at twice P’s distance when the current triples.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Problem 6
A rectangular loop carries a counterclockwise current as viewed in the page. It is first isolated, then placed in a uniform external field pointing rightward in the page.
Part a
State the direction of the loop’s own field at its center. Explain why this should not be used as the external field in calculating the loop’s force.
Part b
The loop has vertical side length 0.0600 m, horizontal side length 0.100 m, I = 2.00 A, and external B = 0.300 T rightward. Find the force on each vertical side and the net force on the whole loop. Can it turn?
Part c
Two long parallel wires carry equal currents out of the page. Explain the net field at their midpoint; then reverse one current while keeping its magnitude unchanged.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Problem 7
A single loop of area 0.0400 m² has its chosen normal out of the page. The field is normal to it: +0.20 T at t = 0, +0.50 T at t = 0.30 s, constant until t = 0.60 s, then −0.10 T at t = 0.90 s. Each transition is linear.
Part a
Calculate signed flux at each listed time. Explain the negative final value and state how the normal is chosen for an open loop versus a closed surface.
Part b
Create a quantitative emf-versus-time graph with labeled axes, units, a suitable vertical scale, and the three interval levels from t = 0 to 0.90 s. State current circulation in each interval if R = 4.00 Ω, and define positive circulation.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Problem 8
A conducting rod of length 0.150 m moves right at 2.00 m/s on rails joined at the left. B = 0.600 T points into the page and total resistance is 3.00 Ω.
Part a
Derive the emf from the area change, then calculate emf and current. Give the current direction.
Part b
Find the external force and power needed for constant speed; independently check the power using electrical heating.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Problem 9
A low-current Hall sensor measures a straight wire’s field. Positive carriers drift horizontally right at 12.0 m/s. The sensor’s transverse width is w = 0.0200 m, measured vertically in the page, perpendicular to that drift. At the sensor the wire field is into the page.
Part a
Predict which sensor edge has higher electric potential. At equilibrium derive the transverse voltage magnitude in terms of v, B, and width w.
Part b
The Hall voltage is 6.00 μV when the sensor is 0.0400 m from a long wire. Estimate wire current. Predict voltage at twice the distance if sensor orientation and carrier speed remain fixed.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Problem 10
Design a hands-on test of B ∝ I/r using a long straight insulated wire, a low-voltage current-limited supply, ammeter, magnetic-field probe, and ruler. Earth’s field and probe offset are not negligible.
Part a
Give a procedure that isolates the wire field, controls geometry, and tests both current dependence and distance dependence.
Part b
At I = 2.00 A, r values of 0.0200, 0.0400, and 0.0800 m give isolated fields 20.4, 9.8, and 5.1 μT. Compute Br for each. Identify a major uncertainty and a justified conclusion.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Problem 11
A vertical conducting rod, perpendicular to two horizontal rails joined at the left, slides right and increases their enclosed area. Uniform B = 0.500 T points into the page, normal to the rail-loop plane; rod length ℓ = 0.100 m, motion, and B are mutually perpendicular. First an effectively open circuit with a high-resistance voltmeter measures emf; then a resistor closes the circuit with total R = 2.00 Ω and the external pulling force is measured. Compare steady test speeds v = 1.00 m/s and 2.00 m/s. For the ideal table neglect friction, rail/rod resistance beyond the stated total, and self-induction; part (b) considers possible experimental friction.
Part a
Construct a numerical table of emf, closed-circuit current, resisting magnetic-force magnitude, and mechanical power at both speeds. Derive the symbolic speed dependence of power from the rod emf and wire-force relationships, then explain why power does not scale linearly with speed.
Part b
State what would change if the circuit were opened, and propose a measurement that distinguishes friction from induction-related resistance.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
More chapter problems
Try these problems before opening the solutions. Show the physical model, your calculation or sketch, and the reason your conclusion follows.
From circular charge motion to a magnetic material
A classical charge +4.00 nC circulates counterclockwise once every 2.00 μs as viewed along the loop axis. Separately, an iron sample and an aluminum sample are placed in the same external magnetic field and then removed. These are distinct classical-loop and material experiments.
(a) Calculate the equivalent conventional current. Explain why the circular charge motion produces a magnetic dipole and determine its central field direction and the polarity of the face you view. Then predict both directions if the circulating charge is negative with the same magnitude and motion.
(b) Explain how electron motion can contribute magnetic dipoles in matter. Assess the statement “electron spin means a tiny charged sphere physically rotating”; distinguish the classical orbital/circulating-charge analogy from intrinsic spin.
(c) Use the configuration of dipoles and domains to explain why the iron may retain magnetization whereas aluminum has only weak temporary magnetization. State what happens to the paramagnetic alignment after field removal, and explain whether the diamagnetic contribution is absent from iron.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Worked solution and rubric →Revisit the explanation →Revisit the explanation →Read the relevant lesson →
Connect a field map to its inverse-distance graphs
A long wire in air carries 4.00 A out of the page. Measure at P to the right of its axis at r = 0.0200, 0.0400, and 0.0800 m, outside the wire and far from its ends. Use μ₀ = 4π × 10⁻⁷ T·m/A.
(a) Draw an arrowed field map around the wire, showing tangent directions at its right, top, left, and bottom. Explain whether B has radial or wire-parallel components, and calculate B at the three specified radii.
(b) Create B-versus-r and B-versus-1/r graphs using all three points. Supply numerical axes, scales, and units; distinguish the inverse curve from a straight fit. Determine the straight-line slope with units. Explain why its origin does not describe r = 0. Predict B at r = 0.0800 m if the current becomes 12.0 A.
Written working workspace
Drawing is temporarily unavailable. Work on paper if needed, then record your reasoning here.
Saving written working requires JavaScript. Keep your work on paper or in your own notes; the source problem above remains available.
Worked solution and rubric →Revisit the explanation →Revisit the explanation →Read the relevant lesson →