Animated Solution for Physics - Magnetic Effects of Current: The magnetic field lines due to a bar magnet are correctly shown in

Imagine you are holding a simple bar magnet in your hand. It has a North pole at one end and a South pole at the other. If you were to sprinkle iron filings around it, you would see a beautiful, symmetric pattern emerge. But what exactly is the fundamental law governing these invisible lines of force?

To understand this, we must first look at a crucial difference between electric and magnetic fields. In electrostatics, electric field lines originate from positive charges and terminate at negative charges. You can have an isolated positive charge, which we call an electric monopole.

However, in the realm of magnetism, things are profoundly different. Magnetic monopoles simply do not exist in nature. You cannot isolate a North pole from a South pole. If you break a magnet in half, you just get two smaller magnets, each with its own North and South pole.

Because there are no magnetic charges to start or end on, magnetic field lines can never have a beginning or an end. They must form continuous, unbroken, closed loops. This profound truth is mathematically elegantly captured by Gauss's Law for Magnetism:

Let's trace the journey of a magnetic field line. We will start by looking at the space outside the magnet.

By convention, magnetic field lines are defined to emerge from the North pole. They burst outward into the surrounding space, curving gracefully around the body of the magnet.

After completing their arc through the air, these lines seek out the opposite pole. They converge and enter the magnet at the South pole. So, if you are placing a compass anywhere outside the magnet, the needle will align itself along these lines, pointing away from the North and towards the South.

Now, here is where many students make a classic mistake. It is tempting to think that the field lines just stop once they hit the South pole, much like electric field lines stopping at a negative charge.

But remember our golden rule: magnetic field lines must form closed loops! They cannot simply vanish.

To complete the loop, the field lines must continue their journey inside the body of the magnet itself. They travel straight through the magnetic material, moving from the South pole back up to the North pole.

This internal path perfectly connects the end of the external journey back to its beginning, creating a seamless, continuous loop.

Armed with this complete picture, let's evaluate the diagrams provided in the options.

We are looking for a diagram that satisfies two strict conditions. First, the arrows on the lines outside the magnet must point from North to South. Second, the arrows on the lines inside the magnet must point from South to North, completing the loop.

If we look at the first option, the lines inside the magnet point from North to South, which would mean the lines are not forming closed loops, but rather originating and terminating at the poles. This violates Gauss's Law for Magnetism.

The third option doesn't even show lines inside, treating them like electrostatic lines.

Only the final diagram correctly illustrates the continuous nature of the magnetic field. The lines flow from North to South on the outside, and from South to North on the inside, forming perfect closed loops.

This exact same pattern is also seen in a current-carrying solenoid, which behaves identically to a bar magnet. Understanding this loop geometry is a foundational stepping stone for mastering electromagnetism!