🧲 المغناطيسية (الوحدة 2 - الكهرباء والمغناطيسية 1)

Magnetic phenomena play an increasingly important role in our daily lives. Simple electrical devices like phones contain a magnet inside, and generators, motors, tape recorders, and computer disks all rely on magnetic effects.

In this activity, we will run an experiment to understand the concept of the magnetic field and derive its properties through observation and analysis.

Materials needed: a magnetism kit (magnetic needles, a bar magnet, a horseshoe magnet).

The magnetic field is represented by imaginary lines called magnetic field lines. The easiest way to find the direction of a field line at any point near a magnet is to place a small compass there: its needle settles so its north pole points toward the magnet’s south pole and its south pole toward the magnet’s north pole, with its axis tangent to the field line.

This simulation draws the field lines and demonstrates the following properties:

• Magnetic field lines are imaginary lines forming closed paths.
• They go from the north pole to the south pole outside the magnet, and from south to north inside it.
• The field direction at any point is tangent to the field line there.
• Field lines never cross.
• Lines are densest at the poles and sparsest at the middle, and their density increases when an iron core is placed inside.

When an iron core is placed inside a current-carrying solenoid, the total magnetic field inside the coil increases due to the magnetic properties of the iron core.

The ratio of the total magnetic field (with the core) to the original field (without the core) is called the magnetic permeability factor (n).

Where: n is a dimensionless number (no unit) that depends on the material’s nature and its ability to be magnetized, and on the magnetizing field B. B_t is the total field (with the core), in tesla. B is the original field (without the core), in tesla.

The larger n is, the greater the material’s ability to concentrate the field lines, and hence the larger the total field.

The Earth behaves like a giant bar magnet: it has two magnetic poles, its axis is tilted about 11° from the Earth’s rotation axis, and the north magnetic pole is not at the same location as the geographic north pole.

In 1820, the Danish scientist Hans Ørsted discovered, during an important experiment, that a magnetic needle deflects when brought near a current-carrying wire. From this he concluded that magnetic fields arise from small currents caused by motion inside the atoms of matter.

In this simulation you see a wire carrying a current; set the current’s direction. To find the field direction, apply the right-hand grip rule: point the thumb along the conventional current, and the fingers curl in the direction of the field. Watch the iron filings and the compass, and try changing the current direction to see how the field direction changes.

When a current flows in a wire, a magnetic field develops around it. Its strength (B) can be expressed in terms of the current (I) and the distance from the wire (d). Below we examine two basic experiments that derive the mathematical relationships, with precise graphs.

In an experiment using a straight wire, the field strength B was measured at a fixed point while the current I was varied. Results below; field values are in \(10^{-4}\;T\).

🔎 General conclusion: the magnetic field is directly proportional to the current in the wire: \(B\propto I\Rightarrow B=kI\).

where k is a constant related to the circuit’s geometry (distance from the wire, shape of the wire), given for a long straight wire by:

(d is the perpendicular distance from the wire.)

Experimental data: constant current \(I=20\;A\), field measured at different distances.

✏️ Required: complete the table by computing \(k=\dfrac{B}{I}\) and \(k'=B\cdot d\)

📊 We note that \(k=B/I\) is not constant (it changes with d), while \(d\times B\) is constant. This confirms that B is inversely proportional to d.

Combining \(B\propto I\) and \(B\propto\dfrac1d\) gives:

The constant is determined experimentally and equals \(\mu_0=4\pi\times10^{-7}\;T\cdot m/A\).

Where: B is the field strength (tesla), I the current (amperes), d the perpendicular distance from the wire (meters), and \(\mu_0\) the permeability of free space \(=4\pi\times10^{-7}\;T\cdot m/A\).

When a current flows in a circular wire (loop):

• A magnetic field is produced perpendicular to the plane of the loop.
• Its direction follows the right-hand rule.
• The field depends on: the current (I), the loop’s radius (r), and the number of turns (N).

Where: \(\mu_0\) is the permeability of free space \((4\pi\times10^{-7}\;T\cdot m/A)\), n the number of turns, I the current (A), r the radius (m).

A current in a circular coil produces a magnetic field along concentric circles around it, and a uniform field at the center of the coil.

In a lab experiment, a steady current \(I=10\;A\) flows in a circular coil of radius \(r=10\;cm\), and the field at the coil’s center is measured with a tesla-meter. The experiment is repeated for identical-radius coils with different numbers of turns (N). Results:

From the table above, B is directly proportional to N. From other experiments, B is also directly proportional to I and inversely proportional to r. Mathematically:

Using the appropriate constant involving the permeability of free space \(\mu_0=4\pi\times10^{-7}\;T\cdot m/A\), we reach the exact law:

The relation can be written in terms of the proportionality constant k: \(B=kI\) where \(k=2\pi\times10^{-7}N/r\).

Given: a straight wire carries a current of \(6\;A\); part of it is bent into a circular loop of radius \(3\;cm=0.03\;m\), one turn \((N=1)\). Find the net field at the center of the loop, accounting for the remaining straight part of the wire (assume it is long, so its field also acts at the center).

Solution:

Field due to the circular loop:

Field due to the straight wire: the straight wire is treated as long (semi-infinite) since the loop is small. The field at a distance \(d=r=0.03\;m\):

Direction of both fields: by the right-hand rule, both fields (from the loop and from the straight wire) point in the same direction at the loop’s center (out of the page), so we add them:

A solenoid is a wire wound into a helical coil (many closely-spaced consecutive turns). When current flows through it, a nearly-uniform magnetic field is produced inside it, parallel to the solenoid’s axis, and it behaves like a bar magnet with a north and a south pole.

If the solenoid has length L and total turns N, the number of turns per unit length is \(n=\dfrac{N}{L}\), and the field inside the solenoid (away from its ends) is:

Where \(\mu_0=4\pi\times10^{-7}\;T\cdot m/A\), I the current, L the length, N the number of turns. Important note: the field inside a long solenoid does not depend on its radius — only on n and I.

The blue lines inside the coil represent the uniform field (from S to N), and the red lines outside represent the field lines returning from N to S — just like a bar magnet. Click the button to reverse the current direction and watch the poles swap and every arrow flip:

Magnetic flux \(\Phi\) expresses the “amount” of magnetic field lines passing through a given area. It depends on the field strength B, the surface area S, and the angle α between the field and the normal to the surface.

The unit of magnetic flux is the weber \((Wb)\); \(1\;Wb = 1\;T\cdot m^2\). Flux is maximum when the field is perpendicular to the surface \((\alpha=0°,\ \cos\alpha=1)\), and zero when the field is parallel to the surface \((\alpha=90°,\ \cos\alpha=0)\).

Change the field strength B, the surface area S, and the tilt angle α, and watch how the surface’s “effective projection” in front of the field lines — and the resulting magnetic flux — change:

For a loop of area \(S=0.05\;m^2\) placed in a uniform field \(B=0.2\;T\), complete the flux \(\Phi\) values for the following angles:

Why are some materials (like iron) strongly magnetic while others (like copper) are practically non-magnetic? The answer lies in the motion of electrons inside the atom:

• Each electron orbits the nucleus (orbital motion) and also spins about its own axis (spin), and both motions act as a microscopic current producing a small magnetic field (an “atomic magnet”).
• In most materials, these atomic magnets are randomly oriented and cancel each other, so the material shows no net magnetic field (like copper).
• In ferromagnetic materials like iron, nickel, and cobalt, atomic magnets cluster into small regions called magnetic domains, and within each domain the atomic magnets align in the same direction.
• In an unmagnetized piece, the different domains point in random directions and cancel out. When the piece is placed in an external field (or brought near a magnet), the domains align in the same direction, and the piece becomes magnetized.

Choose the material, then switch on the external field to see how the magnetic domains inside each material respond:

Because magnetism fundamentally arises from moving charges (electron spin and orbital motion), and every atomic magnet always has two inseparable poles. Cutting a bar magnet in two does not give one piece with only a north pole and another with only a south pole — each piece develops its own new pair of poles, since each piece still contains millions of two-poled atomic magnets.

Strong heating increases thermal vibration of the atoms, and striking causes mechanical disturbance — both disrupt the ordered alignment of the magnetic domains, returning them to random orientations, cancelling the material’s net field.

Soft iron magnetizes easily when current flows (high magnetic permeability) and quickly loses its magnetism when the current stops (little residual magnetism), which suits an electromagnet that must switch on and off with the current. Steel instead retains permanent magnetism after the field is removed, making it suitable for permanent magnets, not electromagnets.