A long, hollow cylinder with inner radius R1 and outer radius R2 carries current along its length. The current is uniformly distributed over the cross-sectional area of the cylinder and has current density J.
1. Find the magnetic-field magnitude B as a function of the distance r from the conductor axis for points inside the hollow interior (r<R1). Express your answer in terms of the variables R1, R2, J, and r.
2. Find the magnetic-field magnitude B as a function of the distance r from the conductor axis for points inside the solid conductor (R1<r<R2). Express your answer in terms of the variables R1, R2, J, and r.
3. Find the magnetic-field magnitude B as a function of the distance r from the conductor axis for points outside the conductor (r>R2).
Current enclosed in the Cylinder is is
Ampere's law
1)
Inside the hollow interior of cylinder,
Charge enclosed in hollow region of cylinder is zero,


2)
For the amperean loop inside the solid conductor,
Charge enclosed is



3)
For the amperean loop outside the conductor,
Charge enclosed is



A long, hollow cylinder with inner radius R1 and outer radius R2 carries current along its...
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As shown in the figure, a long, hollow, conducting cylinder of
inner radius a and outer radius b carries a
current that is flowing out of the page. Suppose that a =
4.13 cm, b = 7.83 cm, and the current i = 273 mA,
uniformly distributed over the cylinder wall (between a
and b). Find the magnitude of the magnetic field at each
of the following distances r from the center of the
cylinder:
As shown in the figure,...
A long, hollow, cylindrical conductor (inner radius 2.0 mm, outer radius 4.0 mm) carries a current of 49 A distributed uniformly across its cross section. A long thin wire that is coaxial with the cylinder carries a current of 55 A in the opposite direction. What is the magnitude of the magnetic field (a) 1.2 mm. (b) 2.1 mm, and (c) 4.0 mm from the central axis of the wire and cylinder?
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Cross-sectional View (current into page) A section of a long conducting cylinder with inner radius a and outer radius b carries a current lo that has a uniform current density, as shown in the figure above. (a) Using Ampère's law, derive an expression for the magnitude of the magnetic field in the following regions as a function of the distance r from the central axis. t. r<a ii. a<r<b (b) On the cross-sectional view in the diagram above, indicate the...
As shown in the figure, a long, hollow, conducting cylinder of
inner radius a and outer radius b carries a
current that is flowing out of the page. Suppose that a =
4.49 cm, b = 7.85 cm, and the current i = 127 mA,
uniformly distributed over the cylinder wall (between a
and b). Find the magnitude of the magnetic field at each
of the following distances r from the center of the
cylinder:
a) r = 6.49 cm.
As shown in the figure, a long, hollow, conducting cylinder of
inner radius a and outer radius b carries a
current that is flowing out of the page. Suppose that a =
4.07 cm, b = 7.23 cm, and the current i = 221 mA,
uniformly distributed over the cylinder wall (between a
and b). Find the magnitude of the magnetic field at each
of the following distances r from the center of the
cylinder:
a) r = 6.05 cm....