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The current density in a cylindrical wire of radius R = 2.0 mm is uniform across a cross section of the wire and is J = 2.0*105 A/m2. What is the current through the outer portion of the wire between the radial distances R/2 and R?Suppose, instead, that the current density through a cross section varies with the radial distances r as J = ar2 in which a = 3.0*1011 A/m2 and r is in meters. What now is the current through the same outer portion of the wire?

The current density in a cylindrical wire of radius R = 2.0 mm is uniform across a cross section of the wire and is J = 2.0*105 A/m2. What is the current through the outer portion of the wire between the radial distances R/2 and R?Suppose, instead, that the current density through a cross section varies with the radial distances r as J = ar2 in which a = 3.0*1011 A/m2 and r is in meters. What now is the current through the same outer portion of the wire?

Grade:12

1 Answers

Shailendra Kumar Sharma
188 Points
6 years ago
CURRENT THROUGH A SMALL AREA (dS) ON A  SURFACE IS GIVENI BY  = J.(dS)
IN ABOVE PRB = CURRENT(I) = J * PI( R^2 – (R/2)^2)
= 2.0*105*3.14(4-1)*10^-3
IN THE SECOND CASE CURRENT CAN BE FOUND BY USINIG  A SMALL CIRCULAR ELEMENT OF RADIUS (dr) = Area of small circular portion is(dS) = (2*pi*r)*dr
current through this portion is  = J.dS = ( a*r^2)*(2*pi*r)*dr
after integrating J.dS from R/2 TO R WE CAN FIND CURRENT THROUGH OUTER PORTION.

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