Question

The formula for determining the magnetic field around a straight conductor is B = μ₀ * (I / (2 * π * r)), where B is the magnetic field in Teslas, μ₀ is a constant called the vacuum permeability, I is the current in Amperes, and r is the radial distance in meters. Which transformed equation can be used to determine the radial distance, r, needed to create a specified magnetic field with a given current?

Answer 1

The equation r = μ₀ * (I / (2 * π * B)) can be used to calculate the necessary radial distance r to create a specified magnetic field around a long straight conductor with a given current, using the value of μ₀ as 4 × 10⁻⁷ T⋅m/A.

Step-by-step explanation:

To find the radial distance r, needed to create a specified magnetic field with a given current for a long straight wire, the original equation B = μ₀ * (I / (2 * π * r)) can be rearranged to solve for r. This rearrangement yields the equation r = μ₀ * (I / (2 * π * B)). Here, μ₀ represents the permeability of free space which has a value of 4 × 10⁻⁷ T⋅m/A, I is the current in amperes, and B is the magnetic field in teslas.

The direction of the magnetic field can be determined by the right-hand rule, where the thumb points in the direction of the current, and the fingers show the direction of the magnetic loops around the wire