To find the magnitude of the conduction current density for a given magnetic field intensity, we can use the equation:

J = σE + Jm

Where J is the conduction current density, σ is the conductivity of the material, E is the electric field intensity, and Jm is the magnetization current density.

Given the magnetic field intensity vector as yi zj xk, we can determine the electric field intensity vector by using Faraday's law of electromagnetic induction:

∇ x E = -∂B/∂t

Where ∇ x E is the curl of the electric field intensity and ∂B/∂t is the partial derivative of the magnetic field intensity with respect to time.

Since the magnetic field intensity vector is given as yi zj xk, we can calculate the curl of the electric field intensity as follows:

∇ x E = ∂Ey/∂z - ∂Ez/∂y xi + ∂Ez/∂x - ∂Ex/∂z yj + ∂Ex/∂y - ∂Ey/∂x zk

Using the equation ∇ x E = -∂B/∂t and comparing the coefficients of the unit vectors, we can determine the partial derivatives of the electric field intensity:

∂Ey/∂z = -∂Bx/∂t
∂Ez/∂y = -∂Bx/∂t

∂Ez/∂x = -∂By/∂t
∂Ex/∂z = -∂By/∂t

∂Ex/∂y = -∂Bz/∂t
∂Ey/∂x = -∂Bz/∂t

Since the magnetic field intensity vector is given as yi zj xk, we can substitute the values into the above equations:

∂Ey/∂z = -0
∂Ez/∂y = -0

∂Ez/∂x = -0
∂Ex/∂z = -0

∂Ex/∂y = -0
∂Ey/∂x = -0

Therefore, the electric field intensity vector is zero.

Next, we need to calculate the magnetization current density, Jm. The magnetization current density is given by:

Jm = ∇ x M

Where M is the magnetization vector.

Since the magnetic field intensity vector is given as yi zj xk, we can determine the curl of the magnetization vector as follows:

∇ x M = ∂My/∂z - ∂Mz/∂y xi + ∂Mz/∂x - ∂Mx/∂z yj + ∂Mx/∂y - ∂My/∂x zk

Since the magnetization vector is not given, we cannot determine the values of the partial derivatives of M. Therefore, we cannot calculate the magnetization current density, Jm.

Finally, we can calculate the conduction current density, J, using the equation J = σE. Since the electric field intensity vector is zero, the conduction current density will also be zero.

Therefore, the magnitude of the conduction current density for a magnetic field intensity of