Suppose B in a region of space centered on the origin has cylindrical symmetry and is given by B = B, ộ where Bo is a constant, and ô is the azimuthal direction in cylindrical coordinates. i) What is the current density in this region of space? ii) Suppose the current density that you found extends out to a radius R and is zero for r>R. What is the magnetic field for r > R?

Problem 2 Show that in a current-free volume of space, a static magnetic field can never have a local maximum by considering V(B· B) · da, where S is the surface of a small volume V containing a point P in space.

▸ Part A What value of magnetic field would make a beam of electrons, traveling to the right at a speed of 5.4×100 m/s. go undeflected through a region where there is a uniform electric field of 9400 V/m pointing vertically up? Express your answer to two significant figures and include the appropriate units. B = 1.7x10-3 T Submit ✓ Correct Part B Previous Answers Part C What is the frequency of the circular orbit of the electrons if the electric field is turned off? Express your answer to two significant figures and include the appropriate units. HA f- Value Submit Request Answer Units ?

A (8.42x10^-1)-m radius cylindrical region contains a uniform electric field along the cylinder axis. It is increasing uniformly with time. What is the rate of change (magnitude) of the electric field required to obtain a total displacement current of (2.047x10^0) nA through a cross section of the region? Provide your answer in V/(m.s) with three significant figures.