The figure below represents a section of a circular conducto

The figure below represents a section of a circular conductor of nonuniform diameter carrying a current of I=5.30 A. The radius of cross-section A_1 is r_1 = 0.500 cm. What is the magnitude of the current density across A_1? The radius r_3 at A_2 is larger than the radius r_1 at A_1. Is the current at A_2 larger, smaller, or the same? The current is larger. The current is smaller. The current is the same. Is the current density at A_2 larger, smaller, or the same? The current density is larger. The current density is smaller. The current density is the same. Assume A_2=5A_1. Specify the radius at A_2. Specify the current at A_2. Specify the current density at A_2.

Solution

a ) J1 = I/A1 = 5.30 / (0.005 m)² = 67481.7 A/m² .

b ) The current is the same

c ) the current density is smaller because it is inversely proportional to area.

if A2 = 5 A1 then r2 = 5 r1

d ) hence, r2 = 5 r1 = 11.18 mm

e ) The current is the same, so I = 5.30 A

f ) current density is, J2 = I/A2 = I/5A1= 5.30 / 5*(0.005 m)² = 13496.34 A/m² .