Section 5.1: Magnetic Fields
Magnetic fields are created by moving charges or currents. The direction of the magnetic field can be determined by the right-hand rule. Magnetic field strength is measured in teslas (T).
- Magnetic Field Due to a Long Straight Wire: \[ B = \frac{\mu_0 I}{2\pi r} \] where \( I \) = current, \( r \) = distance from wire, \( \mu_0 = 4\pi \times 10^{-7} \, \text{T·m/A} \)
- Magnetic Field of a Circular Loop: \[ B = \frac{\mu_0 I}{2R} \] at the center of the loop
- Magnetic Field Between Parallel Wires: Fields add or subtract depending on current direction
Example: Magnetic Field Around a Wire
Calculate the magnetic field 0.05 m away from a wire carrying 5 A current.
\[ B = \frac{\mu_0 I}{2\pi r} = \frac{4\pi \times 10^{-7} \times 5}{2\pi \times 0.05} = 2 \times 10^{-5} \, \text{T} \]
Practice Problems
- Calculate the magnetic field at the center of a circular loop of radius 0.1 m carrying 2 A current.
- Two parallel wires 0.2 m apart carry 3 A each in the same direction. Determine the magnetic field at a point midway between them.
- Explain the significance of the right-hand rule in determining magnetic field direction.
- Derive the expression for magnetic field at a distance r from a long straight wire.
- State one practical application of magnetic fields in everyday technology.