Magnetic Vector Potential Calculator
Magnetic Vector Potential Calculator computes A for a current-carrying wire, visualizing vs. distance.
Formulas Used in Magnetic Vector Potential Calculator
The calculator computes the magnetic vector potential for an infinite straight wire along the z-axis with current \\(I\\):
Magnetic Vector Potential:
\\[ \mathbf{A} = -\frac{\mu_0 I}{2\pi} \ln\left(\frac{\rho}{\rho_0}\right) \hat{z} \\]Where:
- \\(\mathbf{A}\\): Magnetic vector potential (Wb/m)
- \\(I\\): Current (A)
- \\(\mu_0 = 4\pi \times 10^{-7} \, \text{H/m}\\): Permeability of free space
- \\(\rho\\): Radial distance from the wire (m)
- \\(\rho_0\\): Reference distance (m)
Magnitude: \\(|\mathbf{A}| = \left| \frac{\mu_0 I}{2\pi} \ln\left(\frac{\rho}{\rho_0}\right) \right|\\)
Example Calculations
Example 1: Wire with 10 A at 0.1 m
Input: \\( I = 10 \, \text{A}, \rho = 0.1 \, \text{m}, \rho_0 = 1 \, \text{m} \\)
\\[
|\mathbf{A}| = \left| \frac{4\pi \times 10^{-7} \cdot 10}{2\pi} \ln\left(\frac{0.1}{1}\right) \right| \approx 4.605 \times 10^{-6} \, \text{Wb/m}
\\]
Result: \\(|\mathbf{A}| \approx 4.605 \, \mu\text{Wb/m}\\)
Example 2: Wire with 10 A at 0.5 m
Input: \\( I = 10 \, \text{A}, \rho = 0.5 \, \text{m}, \rho_0 = 1 \, \text{m} \\)
\\[
|\mathbf{A}| = \left| \frac{4\pi \times 10^{-7} \cdot 10}{2\pi} \ln\left(\frac{0.5}{1}\right) \right| \approx 1.386 \times 10^{-6} \, \text{Wb/m}
\\]
Result: \\(|\mathbf{A}| \approx 1.386 \, \mu\text{Wb/m}\\)