- #1
You're working with the cross product ##\vec{ds} \times \hat r##. How is the angle between ##\vec{ds}## and ##\hat r## related to the angle ##\theta## shown in diagram ##a##?Callumnc1 said:
Thank you @TSny ! I see how they got theta now. :) If we call the angle between ds and r hat as theta 2, then from the definition of the cross product:TSny said:
The magnetic field around a straight conductor is a circular field that surrounds the conductor. This field is generated when an electric current flows through the conductor, following the right-hand rule for its direction.
The direction of the magnetic field around a straight conductor is determined by the right-hand rule. If you point the thumb of your right hand in the direction of the current, the fingers will curl around the conductor in the direction of the magnetic field lines.
The strength of the magnetic field around a straight conductor is directly proportional to the current flowing through the conductor. This means that as the current increases, the magnetic field strength also increases.
The magnetic field strength decreases with increasing distance from the conductor. Specifically, the field strength is inversely proportional to the distance from the conductor, meaning that the further you move away from the conductor, the weaker the magnetic field becomes.
The magnetic field (B) at a distance (r) from a long straight conductor carrying a current (I) is given by the formula: B = (μ₀ * I) / (2π * r), where μ₀ is the permeability of free space (4π x 10⁻⁷ T·m/A).
