A wire of circular cross-section carries current density that is not uniform but varies with distance from the center as j(r)=j0(1-(r/R)2), for radius r in the range 0 < r < R. Here, j0 is a constant with units amperes per square meter, and the radius of the wire is R = 0.49 mm. A) Find an expression for the current enclosed in a cylinder with a radius of r < R. B) If the total current in the wire is I, find an expression for the constant j0, in terms of the other variables in the problem. C) If the total current is 1.5 A, what is the constant j0, in amperes per square meter? D) Find an expression for the magnetic field inside the wire, r < R, in terms of the current I. E) Find an expression for the magnetic field outside of the wire, for r > R. F) For what r, in meters, is the current enclosed maximum? G) What is the maximum value of the enclosed current, in amperes? H) For what r, in meters, is the magnetic field maximized? I) What is the maximum value of the magnetic field, in tesla?
A wire of circular cross-section carries current density that is not uniform but varies with distance from the center as
j(r)=j0(1-(r/R)2),
for radius r in the range 0 < r < R. Here, j0 is a constant with units amperes per square meter, and the radius of the wire is R = 0.49 mm.
A) Find an expression for the current enclosed in a cylinder with a radius of r < R.
B) If the total current in the wire is I, find an expression for the constant j0, in terms of the other variables in the problem.
C) If the total current is 1.5 A, what is the constant j0, in amperes per square meter?
D) Find an expression for the magnetic field inside the wire, r < R, in terms of the current I.
E) Find an expression for the magnetic field outside of the wire, for r > R.
F) For what r, in meters, is the current enclosed maximum?
G) What is the maximum value of the enclosed current, in amperes?
H) For what r, in meters, is the magnetic field maximized?
I) What is the maximum value of the magnetic field, in tesla?
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