Magnetism Chapter 1 Quiz

Magnetic Field

• A magnetic field is defined as the region surrounding a magnet, moving charge, or current-carrying conductor that exerts a force on other magnets or charges.

Magnetic Field Intensity

• Represented by the symbol $B$ and measured in Tesla (SI unit) or Gauss (c.g.s unit).

Oersted Experiment

• Demonstrated the relationship between electric current and magnetism.
• A current-carrying conductor induces a magnetic field, causing a compass needle to align perpendicularly to the conductor.

Magnetic Field Lines

• The formation of closed loops around current-carrying conductors indicates the nature of the magnetic field.

Direction of Magnetic Field

• The right-hand rule indicates that if the thumb points in the direction of the current, the curled fingers point in the direction of the magnetic field.
• The equation for magnetic field due to a current element is ( dB = \frac{\mu_o \cdot I (ds \times \overrightarrow{r})}{4\pi r^3} ).

Current Carrying Conductors

• A circular loop carrying current will cause a compass needle to deflect.
• The deflection direction of the needle depends on the current's direction:
  • Clockwise current results in negative deflection.
  • Counterclockwise current results in positive deflection.

Biot-Savart's Law

• States that the magnetic field intensity ( dB ) at a point is directly proportional to the current ( I ), the length of the current element ( ds ), and ( \sin(\theta) ) while inversely proportional to the square of the distance ( r ).
• Expressed as ( dB = \frac{\mu_o}{4\pi} \frac{I \cdot ds \sin \theta}{r^2} ).

Total Magnetic Field Intensity

• Total magnetic field intensity ( B ) at a point due to a conductor is the integral of ( dB ):
  ( B = \int dB = \int \frac{\mu_0}{4\pi} I (\overrightarrow{dl} \times \overrightarrow{r}) ).

Application of Biot-Savart's Law

• To calculate the magnetic field intensity at the center of a current-carrying circular coil with radius ( a ):
  • Expressed as ( B = \int \frac{\mu_0}{4\pi} I \frac{(d\overrightarrow{l} \times \overrightarrow{r})}{r^2} ).

Magnetic Field Intensity at the Center of a Circular Coil

• Derived using integration:
  • ( B = \frac{\mu_0 I}{2a} ) if there are ( N ) turns: ( B = \frac{\mu_0 NI}{2a} ).

Magnetic Field Intensity at the Center of a Circular Segment

• Focus on determining the magnetic field intensity at point ( O ) caused by a circular segment with current ( I ).

Key Equations

• Magnetic Field Intensity at Coil Center:
  ( B = \frac{\mu_0 NI}{2a} ) (for ( N ) turns).