2 current in a cylinder an infinitely long straight cylinder of radius

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2. Current in a cylinder. An infinitely long straight cylinder of radius b lies parallel to
the z axis and carries a current with a non-uniform density J = Jo (5) 2 for r < b,
where Jo is a constant and r is the radial distance from the cylinder's central axis.
(a) (1 pt) Calculate the total current I flowing along the cylinder.
(b) (3 pts) Find the magnetic field everywhere inside and outside the cylinder as a
function of r. Express your answer in terms of Jo and b.
An infinitely long thin straight wire with uniform linear charge density A is placed
parallel to the cylinder and held fixed in place. The central axes of the wire and
3
cylinder are a distance 36 apart. A particle of charge +q is placed at point P between
the wire and cylinder, with separations as shown in the diagram below.
wire
20
P
cylinder
b
(c) (2 pts) Find the velocity v (magnitude and direction) that should be given to the
particle such that the net force on it vanishes at point P.