Chapter 13 – Magnetic Effects of Current and Magnetism
1. Introduction to Magnetism
Magnetism arises due to moving electric charges.
A stationary charge produces only an electric field, but a moving charge produces both electric and magnetic fields.
2. Magnetic Field
A magnetic field is the region around a current-carrying conductor or magnet in which a magnetic force can be experienced.
Magnetic field is a vector quantity, denoted by $\vec{B}$.
SI unit of magnetic field = Tesla (T)
3. Oersted’s Experiment
Oersted showed that a current-carrying conductor produces a magnetic field around it, proving the connection between electricity and magnetism.
4. Biot–Savart Law
Biot–Savart law gives the magnetic field due to a small current element.
$$
d\vec{B} = \frac{\mu_0}{4\pi} \frac{I\, d\vec{l} \times \hat{r}}{r^2}
$$
- $I$ = current
- $d\vec{l}$ = current element
- $r$ = distance from element
- $\mu_0$ = permeability of free space
5. Magnetic Field due to a Straight Current-Carrying Conductor
$$
B = \frac{\mu_0 I}{2\pi r}
$$
Direction is given by the Right-Hand Thumb Rule.
6. Ampere’s Circuital Law
The line integral of magnetic field around a closed loop is proportional to the current enclosed.
$$
\oint \vec{B} \cdot d\vec{l} = \mu_0 I
$$
7. Magnetic Field due to a Circular Loop
At the center of a circular loop:
$$
B = \frac{\mu_0 I}{2R}
$$
8. Solenoid and Toroid
Magnetic field inside a long solenoid:
$$
B = \mu_0 n I
$$
Field inside a solenoid is uniform and parallel to the axis.
9. Lorentz Force
A charged particle moving in a magnetic field experiences a force.
$$
\vec{F} = q(\vec{v} \times \vec{B})
$$
Force is always perpendicular to velocity.
10. Motion of Charged Particle in Magnetic Field
Radius of circular path:
$$
r = \frac{mv}{qB}
$$
Time period:
$$
T = \frac{2\pi m}{qB}
$$
11. Force on a Current-Carrying Conductor
$$
\vec{F} = I(\vec{L} \times \vec{B})
$$
12. Torque on a Current Loop
$$
\tau = NIAB \sin\theta
$$
- $N$ = number of turns
- $A$ = area of loop
13. Magnetic Dipole Moment
$$
\vec{m} = NIA \hat{n}
$$
14. Magnetic Properties of Materials
| Material | Property |
|---|---|
| Diamagnetic | Weakly repelled |
| Paramagnetic | Weakly attracted |
| Ferromagnetic | Strongly attracted |
15. Earth’s Magnetism
Earth behaves like a giant magnet with magnetic field components:
- Horizontal component ($B_H$)
- Vertical component ($B_V$)
16. Important JEE Traps
- Magnetic force does no work
- Velocity magnitude remains constant
- Force is always perpendicular to velocity
17. Final Revision Checklist
You have mastered this chapter if you can:
- Apply Biot–Savart and Ampere’s law
- Solve motion of charged particle problems
- Calculate force and torque on current loops
- Understand magnetic materials