Question

A long conducting rod of radius R carries a nonuniform current density given by J = J₀r/R, where J₀ is a constant and r is the radial distance from the rod's axis. (Use the following as necessary: J₀, μ₀, r and R.)

Find an expression for the magnetic field strength inside the rod.
Binside =

Answer 1

To find the expression for the magnetic field strength inside the rod, we can use Ampere's Law. Inside the rod, the current density is given by J = J₀r/R. Applying Ampere's Law to a circular loop of radius r inside the rod, we have Binside = (μ₀ * J₀ * r) / 2.

Step-by-step explanation:

To find the expression for the magnetic field strength inside the rod, we can use Ampere's Law. Ampere's Law states that the line integral of the magnetic field around a closed loop is equal to the permeability of free space times the current passing through the loop.

Using this law, we can calculate the magnetic field at a distance r from the axis of the rod.

Inside the rod, the current density is given by J = J₀r/R. To find the net current passing through a circular loop of radius r inside the rod, we can integrate the current density over the area of the loop. Assuming a constant current density over the cross-sectional area of the rod, the net current passing through the loop is J₀πr².

Applying Ampere's Law to a circular loop of radius r inside the rod, we have Binside * 2πr = μ₀ * J₀πr². Solving for Binside, we find Binside = (μ₀ * J₀ * r) / 2.