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4. A long coaxial cable, crossection of which is shown in the figure, is made up of a cylindrical inner wire of radius a and a cylindrical shell shaped coaxial outer wire of inner radius b and outer radius c. The r2 current density with magnitude J = K- is spread over the cross section of the inner wire where the current has out-of-page direction. Outer wire carries uniformly distributed current i = tka³ having into-the-page direction. a) Find the total current of the inner wire iin in terms of i. Find expressions for the magnitude of magnetic field, b) inside the inner wire (r < a) c) between the wires (a c) in terms of µo, i, TI and r. For each case indicate the direction of the magnetic field as well.

4. A long coaxial cable, crossection of which is shown in the figure, is made up of a cylindrical inner wire of radius a and a cylindrical shell shaped coaxial outer wire of inner radius b and outer radius c. The r2 current density with magnitude J = K- is spread over the cross section of the inner wire where the current has out-of-page direction. Outer wire carries uniformly distributed current i = tka³ having into-the-page direction. a) Find the total current of the inner wire iin in terms of i. Find expressions for the magnitude of magnetic field, b) inside the inner wire (r < a) c) between the wires (a c) in terms of µo, i, TI and r. For each case indicate the direction of the magnetic field as well.

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4. A long coaxial cable, crossection of which is shown in the figure, is made up of a cylindrical inner wire of radius a and a cylindrical shell shaped coaxial outer wire of inner radius b and outer radius c. The r2 current density with magnitude J = K- is spread over the cross section of the inner wire where the current has out-of-page direction. Outer wire carries uniformly distributed current i = tka³ having into-the-page direction. a) Find the total current of the inner wire iin in terms of i. Find expressions for the magnitude of magnetic field, b) inside the inner wire (r < a) c) between the wires (a <r < b) d) inside the outer wire (b <r<c) e) outside the outer wire (r > c) in terms of µo, i, TI and r. For each case indicate the direction of the magnetic field as well.
Transcribed Image Text:4. A long coaxial cable, crossection of which is shown in the figure, is made up of a cylindrical inner wire of radius a and a cylindrical shell shaped coaxial outer wire of inner radius b and outer radius c. The r2 current density with magnitude J = K- is spread over the cross section of the inner wire where the current has out-of-page direction. Outer wire carries uniformly distributed current i = tka³ having into-the-page direction. a) Find the total current of the inner wire iin in terms of i. Find expressions for the magnitude of magnetic field, b) inside the inner wire (r < a) c) between the wires (a <r < b) d) inside the outer wire (b <r<c) e) outside the outer wire (r > c) in terms of µo, i, TI and r. For each case indicate the direction of the magnetic field as well.
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According to our guidelines We’ll answer the first 3 subparts of the question since the exact one wasn’t specified. Please submit a new question specifying the one you’d like answered.

Given, 

J=kr2aa. total current of of inner wire, inLet us take an small element ring shape of width dr at a distance r from the centre, dIcurrent flows in this ring. Hence, current density is given byJ=kr2adIdA=kr2adI=kr2adA=kr2a(2πr dr)∫0IindI=2πka∫0ar3dr On solving Iin=kπa32=i2out of the page, where i is the current in outside shell.

b.  Since, we know Ampere's Law

∫B.da=μ0I∫B.da=B. 2πx∫0idI=∫0x2πkar3dri=kπx42a∫B.da=μ0kπx42aB.2πx=μ0kπx42aB=μ0kx34aThe direction will be along tangent of the circle.

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