Derivation of Magnetic Field of a Straight Wire using Biot-Savart Law

Magnetic Field and Vector Potential

• The direction of the magnetic field dB⃗ at point P due to a current element I dl⃗ at the top of the ring is determined by the right-hand rule.
• The components dB sin  nullify each other when calculating the magnetic field at point P because they are perpendicular to each other and cancel out.
• The magnetic field varies inversely with the square of the distance from the wire, according to Eqn.(5), i.e., B ∝ 1/r^2.
• Only dB cos  components add to each other when calculating the total magnetic field at point P because they are parallel to each other and combine to form the total field.
• The formula for the magnetic field at point P due to a small current element along a straight wire is dB = (μ₀I dl sin φ) / (4πr^2).
• The magnetic field at point P, located at a perpendicular distance y from the straight wire, is directed perpendicular to the plane containing the wire and point P.
• The total magnetic field at point P due to the straight wire is obtained by integrating the contributions from all current elements along the wire.
• The distance r from the origin changes with respect to the angle θ as r = y / sin θ, where y is the perpendicular distance from the wire to point P.
• The magnetic field B⃗ can be related to the Magnetic Vector Potential A⃗ through the equation B⃗ = ∇ × A⃗.
• The magnetic field due to a current-carrying long straight wire is described by the Biot-Savart law.
• The vector potential A⃗ is a vector field that generates the magnetic field through the curl operation.
• A⃗ is known as the Vector Potential because it has the potential to generate the magnetic field.

This quiz involves deriving the formula for the magnetic field generated by a straight wire carrying current using the Biot-Savart law. It covers the steps to calculate the magnetic field at a specific point located at a perpendicular distance from the wire.