Magnetism from Electricity
In 1820, Hans Christian Ørsted discovered that a wire carrying an electric current creates a magnetic field ($B$) around it. This discovery laid the foundation for the entire field of electromagnetism.
For a long, straight wire, the magnetic field forms concentric circles around the wire. The strength of this field depends on:
- Current ($I$): A stronger current produces a stronger magnetic field.
- Distance ($r$): The field strength drops off linearly as you move further away from the wire ($1/r$).
The Right-Hand Rule
To determine the direction of the magnetic field, use the Right-Hand Rule:
- Point your right thumb in the direction of the conventional current flow ($+$ to $-$).
- Your fingers will naturally curl in the direction of the magnetic field lines.
The Formula
Where:
B=
Magnetic Field Strength (Tesla, T)=
Permeability of Free Space (4π × 10⁻⁷ T·m/A)I=
Current (Amperes, A)r=
Distance from wire (meters, m)Example Calculation
A wire carries a current of $20 , \text{Amps}$. You want to find the magnetic field strength at a distance of $2 , \text{cm}$ ($0.02 , \text{m}$).
- Constants: $\mu_0 = 4\pi \times 10^{-7} \approx 1.257 \times 10^{-6}$.
- Calculate: $(1.257 \times 10^{-6} \times 20) / (2 \cdot \pi \cdot 0.02) = 0.0002 , \text{Tesla}$.
The magnetic field is $200 , \mu\text{T}$ (about 4-5 times stronger than the Earth's magnetic field).