Magnetic Fields
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AP Physics C: Electricity and Magnetism › Magnetic Fields
Which of the following statements correctly describes the magnetic field lines produced by a permanent bar magnet?
They represent the trajectory that a small charged particle would follow if it were released from rest near the magnet.
They are always parallel to the magnet's axis inside the magnet and form perfect circles outside the magnet.
They form closed loops which, by convention, emerge from the north pole and enter the south pole outside the magnet.
They originate on the north pole and terminate on the south pole, following straight paths inside the magnet.
Explanation
The correct answer is B. A fundamental property of magnetism is that magnetic field lines always form closed loops. They do not have a starting or ending point. By convention, the direction of the field outside the magnet is from the north pole to the south pole, and inside it is from south to north to complete the loop. A is incorrect because the lines do not terminate. C gives an inaccurate description of the field's geometry. D is incorrect; field lines show the direction of force on a magnetic north pole, not the path of a moving charge, whose path also depends on its velocity.
A small magnetic compass is placed at a point in space. The direction that the north-seeking pole of the compass needle points indicates which of the following?
The direction of the magnetic field vector at that point.
The direction of the electric field vector at that point.
The direction of the force that would be exerted on a stationary positive charge.
The direction toward the nearest magnetic south pole.
Explanation
The correct answer is A. By definition, the direction of the magnetic field vector $$\vec{B}$$ at any point is the direction that the north pole of a compass needle would point if placed at that point. C is equivalent to A, but A is the more formal definition of the field vector's direction. B and D relate to the electric field, not the magnetic field.
An imaginary closed spherical surface completely encloses the north pole of a bar magnet while the south pole is outside the surface. What is the net magnetic flux through the spherical surface?
Zero, because all magnetic field lines that exit the surface from the north pole must re-enter it to reach the south pole.
Positive, because a source of magnetic field (the north pole) is enclosed.
Dependent on the exact strength of the magnet and the radius of the sphere.
Negative, because field lines enter the enclosed volume from the south pole inside the magnet.
Explanation
The correct answer is C. According to Gauss's law for magnetism, the net magnetic flux through any closed surface is always zero. This is because magnetic field lines are continuous loops without beginning or end. Even though the north pole is inside, the field lines that emerge from it and exit the surface must loop around and re-enter the surface somewhere else to continue towards the south pole. The total exiting flux is exactly canceled by the total entering flux. A and B would be true for electric flux and charges, but not for magnetic flux. D is incorrect because the result is always zero.
Two bar magnets are held near each other. A repulsive force is observed between them. This observation implies that:
both magnets must be oriented perpendicular to each other.
the north pole of one magnet is near the north pole of the other.
the north pole of one magnet is near the south pole of the other.
one magnet is a permanent magnet and the other is a temporary magnet.
Explanation
The correct answer is B. The fundamental rule of magnetic interaction is that like poles repel each other (north-north or south-south) and opposite poles attract each other (north-south). A repulsive force indicates that two like poles are near each other. A would result in an attractive force. C describes an orientation that would primarily result in torque. D does not determine the nature of the force, only the properties of the magnets.
The mathematical statement $$\oint \vec{B} \cdot d\vec{A} = 0$$ is known as Gauss's law for magnetism. What is the fundamental physical principle that this law represents?
The net magnetic flux through any closed surface is zero because magnetic monopoles have never been observed.
The total magnetic charge enclosed by any surface must be zero because the magnetic field is a conservative field.
The magnetic force on a moving charged particle is always perpendicular to its velocity and the magnetic field vector.
The line integral of the magnetic field around any closed loop is proportional to the electric current passing through the loop.
Explanation
The correct answer is A. Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero. This is a mathematical expression of the experimental observation that there are no magnetic monopoles (isolated north or south poles). Magnetic field lines always form closed loops, so any line entering a closed surface must also exit it. B is incorrect because the magnetic field is not conservative. C describes Ampère's Law, not Gauss's law for magnetism. D describes the magnetic Lorentz force, which is a different concept.
A magnetic compass needle is a small permanent magnet. When used on Earth's surface away from other magnets, its north-seeking pole points towards Earth's geographic North Pole. What can be directly inferred from this observation?
The Earth's core must be a solid, permanently magnetized ferromagnetic material similar to a bar magnet.
The Earth's magnetic pole located near the geographic North Pole has the polarity of a magnetic north pole.
The Earth's magnetic field lines are precisely parallel to the Earth's surface at all latitudes.
The Earth's magnetic pole located near the geographic North Pole has the polarity of a magnetic south pole.
Explanation
The correct answer is A. The north pole of a magnet (like a compass needle) is attracted to, and points toward, a magnetic south pole. Therefore, for the compass to point towards the geographic North, the Earth's magnetic pole in that vicinity must be a magnetic south pole. B is a common misconception. C is incorrect, as the Earth's magnetic field has a vertical component except at the magnetic equator. D is incorrect; the Earth's core is too hot to be a permanent ferromagnet; the field is generated by electric currents in the molten outer core.
An unmagnetized iron rod becomes a temporary magnet when one end is brought near the north pole of a permanent magnet. This phenomenon of induced magnetism in the iron rod is best explained by the:
transfer of electrons from the permanent magnet to the iron rod, causing a current that generates a field.
separation of positive and negative electric charges to opposite ends of the rod.
creation of new magnetic monopoles within the iron that are attracted to the permanent magnet.
alignment of pre-existing, microscopic magnetic domains within the iron by the external magnetic field.
Explanation
The correct answer is C. Iron is a ferromagnetic material, which contains small regions called magnetic domains where the atomic magnetic moments are already aligned. In an unmagnetized state, these domains are randomly oriented. An external magnetic field exerts a torque on these domains, causing them to align with the external field, thus magnetizing the rod. A describes electric polarization. B is incorrect as monopoles do not exist. D is incorrect as there is no significant transfer of charge.
What is a key difference between the properties of static electric field lines and magnetic field lines?
Electric field lines must form closed loops, whereas magnetic field lines can begin and end on magnetic poles.
Static electric field lines can originate or terminate on charges, whereas magnetic field lines always form closed loops.
The principle of superposition applies to magnetic fields from multiple sources, but it does not apply to electric fields.
Electric fields exert forces only on stationary charges, while magnetic fields exert forces only on moving charges.
Explanation
The correct answer is B. This statement reflects the existence of electric monopoles (charges) and the non-existence of magnetic monopoles. Electric field lines start on positive charges and end on negative charges. Magnetic field lines have no beginning or end; they are always continuous loops. A has the relationship reversed. C is incorrect; superposition applies to both electric and magnetic fields. D is partially incorrect; electric fields exert forces on both stationary and moving charges.
When a diamagnetic material is brought near the north pole of a strong magnet, it experiences a weak repulsive force. This repulsion occurs because the external magnetic field:
causes the material to acquire a net negative electric charge, which is then repelled by the north pole.
reverses the polarity of the strong magnet, causing the two north poles to repel each other.
permanently aligns the material's existing atomic magnetic moments in the opposite direction to the external field.
induces atomic magnetic moments in the material that are aligned in the opposite direction to the external field.
Explanation
The correct answer is A. Diamagnetism is a property of all materials where an external magnetic field induces a weak magnetic dipole moment in the atoms that opposes the external field. This induced opposing field leads to a weak repulsive force. B is incorrect because the effect is induced and not permanent, and it's not an alignment of pre-existing moments. C incorrectly mixes electric and magnetic concepts. D is incorrect; the material does not affect the strong magnet's polarity.
A long, thin bar magnet with a north pole at one end and a south pole at the other is carefully broken exactly in the middle. Which of the following describes the result?
One of the pieces remains a magnet with both poles, while the other piece becomes an unmagnetized piece of metal.
Two shorter, but complete, bar magnets are formed, each with its own north and south pole.
The two pieces are no longer magnetic because the physical shock of breaking them randomizes the magnetic domains.
Two separate pieces are formed, one piece having only a north pole and the other piece having only a south pole.
Explanation
The correct answer is B. A direct consequence of the non-existence of magnetic monopoles is that if a magnet is broken, each piece will become a smaller magnet with both a north and a south pole. Magnetic field lines must form closed loops. A describes the creation of monopoles, which is not possible. C is incorrect because while a severe shock can demagnetize a material, breaking it does not automatically do so; the domain alignment largely persists. D is incorrect; both resulting pieces will be magnets.