Question

According to Gauss's Law for Magnetic Fields, all magnetic field lines form a complete loop. Therefore, the direction of the magnetic field \(\vec{B}\) points from \(\quad\) pole to \(\longrightarrow\) pole outside of an ordinary bar magnet and from pole to pole inside the magnet. a) north, south, north, south c) south, north, south, north b) north, south, south, north d) south, north, north, south

Short answer

Answer: The correct direction of the magnetic field is from North pole to South pole outside the magnet and from South pole to North pole inside the magnet.

Step-by-step solution

Identify the pattern of magnetic field lines outside the magnet

The magnetic field lines form loops and outside the magnet, they go from the North pole to the South pole. So, the direction of \(\vec{B}\) outside the magnet is from North pole to South pole.

Identify the pattern of magnetic field lines inside the magnet

According to Gauss's Law for Magnetic Fields, the magnetic field lines need to form a closed loop. Since the magnetic field lines outside the magnet go from North pole to South pole, in order to complete the loop, they must go from South pole to North pole inside the magnet.

Match the given options with the correct direction of the magnetic field

We have now determined that the magnetic field \(\vec{B}\) points from North pole to South pole outside the magnet and from South pole to North pole inside the magnet. Comparing our findings with the given options: a) North, South, North, South - Incorrect b) North, South, South, North - Correct c) South, North, South, North - Incorrect d) South, North, North, South - Incorrect So, the correct answer is option b) North, South, South, North.

Key concepts

Magnetic Field Lines

Magnetic field lines are a visual tool used to represent the direction and strength of magnetic forces around a magnetic object. Much like contour lines on a map, they show the path along which a North magnetic pole would move if placed in the field. The lines are a series of invisible paths that never cross each other and emanate from a magnet's North pole, looping around to its South pole. The density of these lines corresponds to the magnetic field's strength - the closer together they are, the stronger the magnetic field.

When illustrating these paths, remember that magnetic field lines always form closed loops as per Gauss's Law for Magnetic Fields. This law states that the net magnetic flux through a closed surface is zero, which implies that magnetic field lines do not begin or end but rather loop back on themselves. This is fundamentally different from electric field lines, which start at positive charges and end at negative charges.

Magnetic Poles

Magnetic poles are regions at the end of a magnet where the magnetic force is strongest. There are two types of magnetic poles: North and South, which are analogous to the positive and negative charges in electricity. According to the law of magnetism, opposite poles attract each other, while like poles repel. This concept is central to understanding how magnets interact with each other and with magnetic materials.

It's important to note that individual magnetic poles do not exist independently – you cannot have a North pole without a South pole. When a magnet is cut in half, each piece instantly becomes a new magnet, with both a North and a South pole. This inseparability of the magnetic poles is related to Gauss's Law for Magnetic Fields, which implies that isolated magnetic poles, called magnetic monopoles, do not naturally occur.

Magnetostatics

Magnetostatics is the study of magnetic fields in systems where the currents are steady and unchanging. In these systems, the electric charges do not accelerate, and therefore, the magnetic fields are constant over time. This branch of physics is analogous to electrostatics in electricity, where charges are at rest.

In magnetostatics, one of the fundamental principles is that the generated magnetic field depends on the current that produces it, and it is mathematically described by Ampère's Circuital Law and Biot–Savart Law. Gauss's Law for Magnetic Fields holds true in magnetostatics, reinforcing that the magnetic field lines must form closed loops, reflecting the absence of magnetic charges or monopoles. Understanding magnetostatics is essential for applications like electromagnets, transformers, and electric motors, where steady currents generate predictable and stable magnetic fields.