Magnetic Fields
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AP Physics 2 › Magnetic Fields
A circular loop of radius $4.0\ \text{cm}$ lies in the plane of the page and carries a clockwise current of $2.0\ \text{A}$. Which statement best describes the magnetic field direction at the center of the loop?
It points into the page.
It points out of the page.
It points upward in the plane of the page.
It is zero unless a magnetic material is placed at the center.
Explanation
This question tests understanding of magnetic fields. Magnetic fields are vector quantities in space produced by electric currents or permanent magnets that exert forces on other currents or magnets. For a current loop, the magnetic field at the center can be determined using the right-hand rule: curl your right fingers in the direction of current flow, and your thumb points in the field direction. With clockwise current in the plane of the page, your thumb points into the page at the center. Choice D incorrectly assumes magnetic fields require magnetic materials to exist, confusing field detection with field existence. To find the field direction at the center of a current loop, always use the right-hand rule with fingers following the current.
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?
Upward, away from the north pole.
Sideways, because field lines circle around the poles.
Zero because the field exists only between the poles.
Downward, toward the north pole.
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.
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 $B_B$.
$B_A$ depends on whether a compass is placed at $A$.
$B_A$ equals $B_B$ because both points are in air.
$B_A$ is four times $B_B$.
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 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 south (−$y$) by the right-hand rule.
It is zero unless a compass is placed at the point.
It points east (+$x$), following the moving charges.
It points north (+$y$) 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.
Two long parallel wires are $4.0\ \text{cm}$ apart and carry equal currents $I$ upward. Point $M$ is midway between them. Which statement best describes the net magnetic field magnitude at $M$?
It equals the field from one wire because the other is farther.
It depends on the magnetic material placed at point $M$.
It is zero because the fields from the two wires cancel.
It is doubled because the fields from the two wires add.
Explanation
This question tests understanding of magnetic fields. Magnetic fields are vector quantities that add according to vector addition rules, with both magnitude and direction crucial for determining the net field. When two parallel wires carry current in the same direction (both upward), the magnetic fields they produce circulate around each wire following the right-hand rule. At the midpoint between the wires, the field from the left wire points into the page while the field from the right wire points out of the page. Since the wires carry equal currents and the midpoint is equidistant from both, these fields have equal magnitudes but opposite directions, resulting in complete cancellation. Choice B incorrectly assumes fields always add constructively, ignoring that vector addition requires considering direction. When analyzing fields from multiple sources, always determine both magnitude and direction at the point of interest before combining vectors.
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.
Tangent to the loop, following the current’s path.
Zero because the field exists only at the wire itself.
Out of the page by the right-hand rule.
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 long straight wire carries current downward (−$y$). At a point to the east of the wire (+$x$), which statement best describes the magnetic field direction there?
Out of the page (+$z$) by the right-hand rule.
Into the page (−$z$) by the right-hand rule.
Zero unless a moving charge passes through the point.
Downward (−$y$), in the same direction as the current.
Explanation
This question tests understanding of magnetic fields. Magnetic fields circulate around current-carrying wires in a pattern determined by the right-hand rule: point your thumb in the current direction, and your fingers show how field lines wrap around the wire. For current flowing downward (-y), point your thumb down; at a point east of the wire (+x direction), your fingers curl from east toward north, then west, then south, meaning the field points out of the page (+z direction) at the eastern point. The field forms concentric circles centered on the wire, perpendicular to the current direction. Choice C incorrectly assumes magnetic fields point in the same direction as current flow, confusing field orientation with charge motion. Apply the right-hand rule systematically: thumb along current, fingers show field circulation, determining field direction at any point around the wire.
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 $Q$?
$B_P$ equals $B_Q$ because the current is the same.
$B_P$ is three times $B_Q$.
$B_P$ is nonzero only at the wire’s surface.
$B_P$ is one-third of $B_Q$.
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 bar magnet lies horizontally with its north pole on the left and south pole on the right. At a point on the axis to the right of the south pole, which statement best describes the magnetic field direction?
It points to the right, away from the south pole.
It points upward because field lines rise off the magnet.
It points to the left, toward the south pole.
It exists only inside the magnet, so it is zero there.
Explanation
This question tests understanding of magnetic fields. Magnetic fields emerge from the north pole of a magnet and enter the south pole, forming continuous closed loops through and around the magnet. Outside a bar magnet, field lines point away from the north pole and toward the south pole. At a point on the axis to the right of the south pole, the field continues in the same direction it had between the poles—pointing left toward the south pole. Choice C incorrectly assumes field lines rise vertically off magnets, confusing the 3D nature of field patterns with a simplified 2D representation. Remember that magnetic field lines outside a magnet always point from north to south poles, continuing the pattern established between the poles.