Magnetic Fields
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AP Physics 2 › Magnetic Fields
A long straight wire carries a steady current of $3.0\ \text{A}$ upward (along $+y$). Points $P$ and $Q$ are in the plane of the page, each $2.0\ \text{cm}$ from the wire, with $P$ to the right of the wire and $Q$ to the left. Which statement best describes the magnetic field direction at point $P$?
It points out of the page at $P$.
It is zero at $P$ because magnetic fields exist only at the wire’s surface.
It points upward because field lines follow the current’s path.
It points toward the wire at $P$.
Explanation
This question tests understanding of magnetic fields. Magnetic fields are invisible properties of space created by moving charges or permanent magnets that exert forces on other moving charges or magnetic materials. For a long straight wire carrying current, the magnetic field forms concentric circles around the wire, with the field direction determined by the right-hand rule: point your right thumb along the current direction, and your fingers curl in the direction of the magnetic field. With current flowing upward and point P to the right of the wire, the field at P points out of the page. Choice C incorrectly assumes field lines follow the current's path, confusing the field pattern with current flow. To determine field direction around a current-carrying wire, always use the right-hand rule rather than assuming fields point along or toward the current.
A circular loop of radius $R$ lies in the page and carries current counterclockwise. Which statement best describes the magnetic field direction at the loop’s center?
Into the page by the right-hand rule.
Zero because the field exists only at the wire itself.
Out of the page by the right-hand rule.
Tangent to the loop, following the current’s path.
Explanation
This question tests understanding of magnetic fields. Magnetic fields are produced by moving charges, and their direction follows specific rules based on the current configuration. For a circular current loop, use the right-hand rule: curl your fingers in the direction of current flow (counterclockwise when viewed from above), and your thumb points in the direction of the magnetic field at the center. Since the current flows counterclockwise in the page, your thumb points out of the page at the loop's center. Choice C incorrectly assumes the magnetic field follows the current's path, confusing field direction with charge motion—magnetic fields are perpendicular to current flow, not parallel. To find the field direction at the center of a current loop, curl your right-hand fingers along the current direction; your thumb shows the field direction.
A bar magnet is vertical with north at the top and south at the bottom. At a point just above the north pole on the axis, which statement best describes the magnetic field direction?
Zero because the field exists only between the poles.
Downward, toward the north pole.
Upward, away from the north pole.
Sideways, because field lines circle around the poles.
Explanation
This question tests understanding of magnetic fields. Magnetic field lines emerge from the north pole of any magnet and curve around to enter the south pole, forming continuous closed loops. At a point on the axis just above the north pole, the field lines are emerging from the pole and pointing upward, away from the magnet. This is true for any magnet configuration—field lines always exit north poles and enter south poles. Choice C incorrectly assumes field lines circle around individual poles like they do around current-carrying wires, confusing the field patterns of magnets with those of currents. Remember that magnetic field direction at any point near a magnet can be found by following the field line passing through that point, always flowing from north to south outside the magnet.
Two long parallel wires are $6.0\ \text{cm}$ apart. The left wire carries $4.0\ \text{A}$ upward, and the right wire carries $4.0\ \text{A}$ upward. Point $M$ is midway between them. Which statement best describes the magnetic field magnitude at point $M$ due to the two wires?
It is maximum because the fields from the two wires add in the same direction there.
It is zero because the fields from the two wires are equal in magnitude and opposite in direction there.
It depends on whether a compass is placed at $M$ to create a field.
It is nonzero only on the surfaces of the wires, so it is zero at $M$.
Explanation
This question tests understanding of magnetic fields. Magnetic fields are vector fields created by moving charges that can superpose when multiple sources are present. For parallel wires carrying current in the same direction, each wire creates a circular magnetic field pattern around itself. At the midpoint M between two wires carrying equal upward currents, the left wire creates a field pointing out of the page while the right wire creates a field pointing into the page. Since these fields have equal magnitudes but opposite directions at M, they cancel completely, resulting in zero net field. Choice B incorrectly assumes fields from same-direction currents always add constructively, missing the geometry of the situation. When analyzing fields from multiple sources, always determine the field direction from each source separately before adding vectors.
A long straight wire carries $5.0\ \text{A}$ upward. Points $A$ and $B$ are $1.0\ \text{cm}$ and $4.0\ \text{cm}$ from the wire. Which statement best compares the magnetic field magnitudes?
$B_A$ is one-fourth of $B_B$.
$B_A$ is four times $B_B$.
$B_A$ equals $B_B$ because both points are in air.
$B_A$ depends on whether a compass is placed at $A$.
Explanation
This question tests understanding of magnetic fields. Magnetic fields around current-carrying wires decrease with distance according to the inverse relationship B = μ₀I/(2πr), where r is the perpendicular distance from the wire. For the same current of 5.0 A, point A at 1.0 cm experiences a field B_A = μ₀I/(2π×0.01), while point B at 4.0 cm experiences B_B = μ₀I/(2π×0.04). Since point B is four times farther from the wire than point A, the magnetic field at B is one-fourth that at A, making B_A four times larger than B_B. Choice B incorrectly assumes the medium (air) determines field strength rather than distance, missing the fundamental inverse relationship. When comparing magnetic fields at different distances, remember that field strength is inversely proportional to distance: quadrupling the distance reduces the field to one-quarter.
A long straight wire carries $3.0\ \text{A}$ upward (toward +$y$). Points $P$ and $Q$ are $2.0\ \text{cm}$ and $6.0\ \text{cm}$ to the right of the wire. Which statement best compares the magnetic field magnitudes at $P$ and $Q$?
$B_P$ is three times $B_Q$.
$B_P$ equals $B_Q$ because the current is the same.
$B_P$ is one-third of $B_Q$.
$B_P$ is nonzero only at the wire’s surface.
Explanation
This question tests understanding of magnetic fields. Magnetic fields are regions of space where magnetic forces can be detected, created by moving charges or permanent magnets. For a long straight wire carrying current, the magnetic field magnitude at distance r is given by B = μ₀I/(2πr), showing an inverse relationship with distance. Since point P is at 2.0 cm and point Q is at 6.0 cm (three times farther), and both experience the field from the same 3.0 A current, B_P = μ₀I/(2π×0.02) and B_Q = μ₀I/(2π×0.06), making B_P three times larger than B_Q. Choice B incorrectly assumes field strength is constant regardless of distance, missing the fundamental inverse relationship between field strength and distance from the source. When comparing magnetic fields at different distances from a current-carrying wire, always apply the inverse proportionality: doubling the distance halves the field, tripling the distance reduces it to one-third.
A long straight wire carries a steady current into the page (along $-z$). Point $N$ is located to the right of the wire in the plane of the page. Which statement best describes the magnetic field direction at point $N$?
It is zero unless a test magnet is present.
It points downward in the plane of the page.
It points to the right because magnetic field lines travel with the current.
It points upward in the plane of the page.
Explanation
This question tests understanding of magnetic fields. Magnetic fields are properties of space around electric currents or magnets that exert forces on other moving charges or magnetic materials. For a wire carrying current into the page, the magnetic field forms circular patterns around the wire following the right-hand rule: point your right thumb into the page (current direction), and your fingers curl clockwise when viewed from above. At point N to the right of the wire, the clockwise field pattern means the field points downward in the plane of the page. Choice A incorrectly assumes magnetic fields travel with the current, confusing field direction with current flow. To find magnetic field direction, use the right-hand rule based on current direction, not assumptions about fields following currents.
A bar magnet lies horizontally with its north pole on the left and south pole on the right. Point $T$ is located just outside the magnet near the midpoint above it. Which statement best describes the magnetic field direction at point $T$?
It points from left to right, from the north pole toward the south pole.
It is zero because magnetic fields exist only at the poles’ surfaces.
It points upward because magnetic field lines are paths that charges would follow.
It points from right to left, from the south pole toward the north pole.
Explanation
This question tests understanding of magnetic fields. Magnetic fields are vector fields in space created by magnets or electric currents that can exert forces on other magnets or moving charges. For a bar magnet, magnetic field lines emerge from the north pole and curve around to enter the south pole, forming closed loops. At point T above the magnet's midpoint, the field lines are curving from the north pole (left) toward the south pole (right), so the field points from left to right. Choice C incorrectly treats magnetic field lines as paths that charges follow, confusing field direction with particle motion. Remember that magnetic field lines show the direction a north pole would be pushed, not the path charges take.
A solenoid is oriented along +$x$ and carries current so that, viewed from the +$x$ end, the turns are counterclockwise. Which statement best describes the magnetic field direction inside the solenoid?
It exists only near the wire windings, not in the interior.
It points radially outward from the solenoid’s axis.
It points in the −$x$ direction.
It points in the +$x$ direction.
Explanation
This question tests understanding of magnetic fields. Magnetic fields inside solenoids are uniform and parallel to the solenoid's axis, with direction determined by the right-hand rule applied to the coil windings. When viewing the solenoid from the +x end and seeing counterclockwise current, curl your right-hand fingers counterclockwise—your thumb points toward you, which is in the +x direction inside the solenoid. The magnetic field inside an ideal solenoid is uniform and axial, quite different from the complex field patterns outside. Choice D incorrectly assumes fields exist only at current locations, missing that magnetic fields fill the space around and within current configurations. For solenoids, use the right-hand rule with fingers following the current in the coils; your thumb indicates the field direction inside.
A long straight wire carries current to the east (+$x$). At a point directly above the wire (+$z$ direction), which statement best describes the magnetic field direction there?
It points north (+$y$) by the right-hand rule.
It points east (+$x$), following the moving charges.
It is zero unless a compass is placed at the point.
It points south (−$y$) by the right-hand rule.
Explanation
This question tests understanding of magnetic fields. Magnetic fields are vector quantities produced by moving charges, with direction determined by the right-hand rule: point your thumb along the current direction, and your fingers curl in the direction of the magnetic field lines. For a wire carrying current east (+x), at a point directly above (+z), wrap your right hand around the wire with thumb pointing east—your fingers curl from above the wire toward the south (-y direction). The magnetic field circles the wire in a specific rotational sense determined by the current direction. Choice C incorrectly assumes the field points in the same direction as the current flow, confusing magnetic field direction with charge motion direction. To find magnetic field direction around a straight wire, use the right-hand rule: thumb along current, fingers show field circulation pattern.