An infinitely long, straight conductor consists of of an inner cylindrical condu

Question

An infinitely long, straight conductor consists of of an inner cylindrical conductor of radius
R which carries a uniform current I0. This conductor is surrounded bv a second, coaxial
conductor of inner radius R and outer radius 2R. Through this outer conductor flows a
uniform current of 2I0, with a direction that is opposite to the one in the central conductor'.
Calculate the magnetic field strength B for the following distances from the center of the
conductor:
a)r>2R
b) R <r <2R
c)r<R

Explanation / Answer

a) at r > 2*R

Apply,

integral B*dl = mue*I_enclosed

B*2*pi*r = mue*(2*Io - Io)

B = mue*Io/(2*pi*r) <<<<<---------Answer

b) R <r <2R

Apply,

integral B*dl = mue*I_enclosed

B*2*pi*r = mue*(2*Io*(r^2 - R^2)/(2*R)^2 - Io)

= mue*Io*((r^2 - R^2)/(2*R^2) - 1 )

B = mue*Io*((r^2 - R^2)/(2*R^2) - 1 )/(2*pi*r) <<<<<---------Answer

c) at r< R

Apply,

integral B*dl = mue*I_enclosed

B*2*pi*r = mue*Io*(r^2/R^2)

B = mue*Io*r/(2*pi*R^2) <<<<<---------Answer

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