Question

A long straight cylindrical wire of radius R is carrying a current density J which is proportional to the square of the distance r from the central axis, i.e. J = kr2 (0 r R), where k is a constant. The total current on the wire is I, as shown in Figure 3. (a) Express the total current I in terms of k and R. (b) Calculate the magnetic field outside the wire (r R). (c) Calculate the magnetic field inside the wire (0 r R)

Name: a long straight cylindrical wire of radius r is carrying a current density j which is proportional to the square of the distance r from the central axis ie j kr2 0 r r where k is a constant the total
Uploaded: 2022-05-10T03:27:19-08:00
Duration: 2 min 41 s
Channel: Timothy James
Description: a long straight cylindrical wire of radius r is carrying a current density j which is proportional to the square of the distance r from the central axis ie j kr2 0 r r where k is a constant the total

          A long straight cylindrical wire of radius R is carrying a current density J which is
proportional to the square of the distance r from the central axis, i.e. J = kr2
(0 r R),
where k is a constant. The total current on the wire is I, as shown in Figure 3.
(a) Express the total current I in terms of k and R. 
(b) Calculate the magnetic field outside the wire (r R). 
(c) Calculate the magnetic field inside the wire (0 r R)

Added by Jun Z.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Timothy James

05/10/2022

Step 1

Step 1: The total current in the wire is given by the integral of the current density over the cross-sectional area of the wire: \[ I = \int_{0}^{R} J \cdot dA = \int_{0}^{R} kR^2 \cdot 2\pi R \, dR = 2\pi k \int_{0}^{R} R^3 \, dR \] \[ I = 2\pi k \left[ Show more…

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A long straight cylindrical wire of radius R is carrying a current density J which is proportional to the square of the distance r from the central axis, i.e. J = kr2 (0 r R), where k is a constant. The total current on the wire is I, as shown in Figure 3. (a) Express the total current I in terms of k and R. (b) Calculate the magnetic field outside the wire (r R). (c) Calculate the magnetic field inside the wire (0 r R)