Chapter 22: Electromagnetism

Magnetic Field

A region around a moving charge or a magnet where magnetic forces can be observed.

Ampère’s Law

The magnetic field around a current-carrying wire is proportional to the current enclosed: ${\oint }_{\text{loop}}B\cdot dl=\mu I_{\text{enclosed}}$

Biot-Savart Law

Describes the magnetic field generated by a segment of current-carrying wire: $\mathrm{dB}=(\mu 0I\times \mathrm{dl}\times r)/r^2$

Magnetic Fields Due to Currents

• Straight Wires: Magnetic fields form concentric circles around the wire. Use the right-hand rule to determine direction.
• Wire Loops: Magnetic field resembles that of a magnetic dipole.
• Solenoid: A series of current loops that create a uniform magnetic field inside.
• Electromagnet: A solenoid with a ferromagnetic core, used to control magnetic flux density.

Electromagnetic Induction

Definition

The generation of an electric current due to a changing magnetic field.

Magnetic Flux (Φ)

The product of magnetic field strength and area through which it passes: $\Phi =B\cdot A\cdot cos\theta$

Applications

• Electromagnets: Used in motors, transformers, and medical equipment.
• Magnetic Flux Measurements: Important in determining the performance of generators and transformers.
• Induction Cooktops: Use changing magnetic fields to directly heat cookware.

Questions for Students

1. Define Ampère’s Law and describe its significance in electromagnetism.
2. Explain how the right-hand rule is used to determine the direction of a magnetic field.
3. Describe the properties and applications of a solenoid.
4. What is electromagnetic induction, and how does it relate to Faraday’s law?
5. Calculate the magnetic flux through a loop of radius 0.2 m in a 0.5 T magnetic field at an angle of 30°.