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Show that the 3D force field is a conservative field. Find the work done against the force when moving from Write down (i) an expression for the gradient of a 3D scalar field Ф(x, y, z) and (ii) the pseudo-determinant expression for the curl of a vector field v. Then show that x17Ф 0 (a zero vector) for any scalar field Ф Verify this result by direct calculation of the curl of F given in the previous question. A cylinder of radius a has its axis of symmetry aligned with the z-axis. Its bottom and top are at z=0 and z = h, respectively. Sketch and give vector values for the outward elements of surface area dS at the cylinder's top, bottom and sidewall. A wire lying along the z-axis holds a charge per unit length of A. The vector electric flux density D has cylindrical radial symmetry and magnitude D(r)-X/(2Tr) Write the vector expression for D and show that D dS-Ah where the integral is over the entire surface of the cylinder.

Answer 1