Q# 01: Calculate Curl and divergence of given vector field F = (3x + 2z²)î + ;- (z – 7x)k

We have calculated the electric field due to a uniformly charged disk of radius R, along its axis. Note that the final result does not contain the integration variable r: R. Q/A 2€0 Edisk (x² +R*)* Edisk perpendicular to the center of the disk Uniform Q over area A (A=RR²) Show that at a perpendicular distance R from the center of a uniformly negatively charged disk of CA and is directed toward the disk: Q/A radius R, the electric field is 0.3- 2€0 4.4.1b

1. The electric field in a region of space near the origin is given by () E(x, y, z) = Eo a (a) Evaluate the curl V x E(x, y, z) (b) Setting V(0, 0, 0) = 0, select a path from (0,0, 0) to (x, y,0) and compute V (x, y, 0).

Suppose a unidirectional vector field E exists across an enclosed surface A as shown below. which among the following is/are true? 153 E The divergence volume integral value will only be equal to 0 if E is a uniform field. O The divergence volume integral value will be positive if the magnitude of E is increasing along the positive z-hat direction. The divergence volume integral value will always be equal to 0. Only the top and bottom cylindrical phases have non-zero divergence surface integral values.