Revision: Magnetism and Magnetic Effects of Electric Current Physics HSC Science Class 12 Tamil Nadu Board of Secondary Education

The magnetic dipole moment is defined as the product of its pole strength and magnetic length.

`vec"P" = "q"_"m"vec"d"`

Ferromagnetism is defined as the phenomenon in which substances, such as iron, cobalt and nickel, are strongly attracted by a magnetic field. Such substances are called ferromagnetic substances.

The lagging of intensity of magnetisation (I) or magnetic induction (B) behind the magnetising field (H) during the process of magnetisation and demagnetisation of a ferromagnetic material is called hysteresis.

The residual value of magnetic induction (B) retained by a ferromagnetic material when the magnetising field (H) is reduced to zero (represented by point B/C on the hysteresis loop) is called retentivity.

The value of the reverse magnetising field (H₀) required to reduce the residual magnetic induction of a ferromagnetic material to zero (represented by point F on the hysteresis loop) is called coercivity.

A current-carrying conductor is always associated with a magnetic field around it is called the magnetic effect of current. It was first discovered by Hans Christian Oersted in 1820.

Current passed through each of the two infinitely long parallel straight conductors kept at a distance of one meter apart in vacuum causes each conductor to experience a force of 2 × 10^-7 newton per meter length of the conductor.

The turning effect experienced by a current-carrying loop placed in a uniform magnetic field, which forms the working principle of a moving coil galvanometer (MCG), is called torque on a current loop.

Combining the four dependencies: dB ∝ \[\frac {I dl sin θ}{r^2}\]​

Introducing the constant of proportionality \[\frac {μ_0}{4π}\]​​:

\[dB=\frac{\mu_0}{4\pi}\cdot\frac{Idl\sin\theta}{r^2}\]

\[{d\vec{B}=\frac{\mu_0}{4\pi}\cdot\frac{Id\vec{l}\times\hat{r}}{r^2}=\frac{\mu_0}{4\pi}\cdot\frac{Id\vec{l}\times\vec{r}}{r^3}}\]

For a finite conductor, integrate over the entire length:

\[{\vec{B}=\frac{\mu_0I}{4\pi}\int\frac{d\vec{l}\times\hat{r}}{r^2}}\]

When a ferromagnetic material is subjected to a cycle of magnetisation and demagnetisation, the intensity of magnetisation (I) or magnetic induction (B) lags behind the magnetising field (H). This lagging behaviour is called hysteresis. When plotted on a B–H graph, the curve forms a closed loop (hysteresis loop) in which:

• B₀​ (point A) denotes the saturation magnetic induction,
• The intercept OB (or OC) on the B-axis when H is reduced to zero represents retentivity (residual magnetism),
• The intercept OF on the H-axis (reverse field H_0​) needed to reduce B to zero represents coercivity,
• Points D and E represent reverse saturation and reverse retentivity respectively.

The area enclosed by the hysteresis loop is equal to the energy loss per cycle per unit volume of the material, and this area is different for different materials. Therefore, materials used as electromagnets require a narrow loop (low hysteresis loss), while permanent magnets require a wide loop (high retentivity and coercivity).

The magnitude of magnetic induction (dB) at a point due to a small element of current carrying conductor is:
(i) directly proportional to current (dB ∝ I),
(ii) directly proportional to length of element (dB ∝ dl),
(iii) directly proportional to sine of angle between element and line joining its centre to the point (dB ∝ sin θ),
(iv) inversely proportional to square of distance (dB ∝ 1/r²).

Applications

• Magnetic field at centre of circular coil.
• Magnetic field on axis of the coil.
• Magnetic field at a distance from a straight current-carrying conductor.

Statement

The line integral \[\oint\vec{B}\cdot d\vec{l}\] taken around any closed loop equals μ₀ times the net steady current passing through the loop.

Proof (for a long straight wire)

• Consider an infinitely long straight wire carrying current I.

• By Biot–Savart law, field at distance r:
  B = \[\frac{\mu_0I}{2\pi r}\]

• Choose a circular Amperian loop of radius r, concentric with the wire.

• By symmetry, B is constant in magnitude and tangential (parallel to \[d\vec l\]) everywhere:
  \[\oint\vec{B}\cdot d\vec{l}=B\oint dl\] = B(2πr)

• Substituting B:
  \[\oint\vec{B}\cdot d\vec{l}=\frac{\mu_0I}{2\pi r}(2\pi r)\] = μ₀​I

Conclusion

\[\oint\vec{B}\cdot d\vec{l}=\mu_0I\]
The result is independent of the loop's radius, confirming the law's validity.

Motion of electrons generates a magnetic field — each electron behaves like a tiny bar magnet with a magnetic moment measured in Bohr Magneton (μ_B) = 9.27 × 10⁻²⁴ A m².

• Electric current creates a magnetic field, shown by compass needle deflection.
• Oersted discovered the link between electricity and magnetism in 1820.
• Reversing current changes the direction of the magnetic field.
• Iron filings form circular patterns, showing magnetic field lines around the wire.
• Magnetic field strength increases with current and decreases with distance.

• Torque depends on current, magnetic field strength and area of the loop.
• For a given perimeter, a circular loop experiences maximum torque (maximum area).
• Forms the working principle of the moving coil galvanometer (MCG).