4.1.1. Find the electric field in the region x > 0 if E = 2 u _x + 2 u _y V/m in the region x < 0. There is no surface charge density.

4.1.2. Repeat Problem 3 with a surface charge density ? _s = 0.5 C/m ².

4.1.3. Find the electric field in the region x > 0. There is no surface charge density. The magnitude of the electric field is 5 V/m.

4.1.4. Repeat Problem 1 with a surface charge density ? _s = 1 C/m ².

4.1.5. Find the magnetic flux density in the region x > 0 if B = 4 u _x + 4 u _y T in the region x < 0. The surface current equals zero.

4.1.6. Repeat Problem 4.1.5 if the surface current density J _s = (9 u _z + 9 u _y) A/m.

4.1.7. Can the indicated electric field exist? If not, suggest how an additional electric field will permit the existence of this field.

4.3.1. Find the potential distribution V( r) by solving Laplace's equation analytically for the region between two concentric hollow spheres (spherical capacitor). Apply a spherical coordinate system with the following boundary conditions: V = 0 at r = a and V = V