3.1.1. Calculate the total current that passes through the indicated surface. The current density J = 3 x u _x + 4 x u _y A/m ².

3.1.2. Calculate the total current that passes through the indicated surface. The current density J = 3 x u _x + 4 x u _z A/m ².

3.1.3. The current density in a cylindrical wire whose radius a is given by

Compute the total current in the wire.

3.1.4. A lightning stroke with a current I = 10 kA strikes a post. Find the voltage V _ab between the legs of a man, situated on a distance a = 5 m from the post, if the step-size is ? = 0.6 m (see the figure). Assume that the ground is homogeneous with conductivity ? = 0.02 S/m.

3.2.1. In terms of the units of mass M, length L, time T, and charge Q, find the units of the permeability ? ₀ of vacuum.

3.2.2. In terms of the units of mass M, length L, time T, and charge Q, show that the units of have the same dimensions as a velocity.

3.2.3. Find and plot the magnetic flux density as a function of radius for the concentric hollow cylinders. The currents are I(