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 = 4.30 A. The radius of cross-section A₁ is r₁ = 0.420 cm.

(a) What is the magnitude of the current density across A₁ (A/m²)?

The radius r₂ at A₂ is larger than the radius r₁ at A₁.

(b) Is the current at A₂ larger, smaller, or the same?

(c) Is the current density at A₂ larger, smaller, or the same?

Assume A₂ = 3A₁

(d) Specify the radius at (A₂).

(e) Specify the current at A₂.

(f) Specify the current density at A₂.

Solution

a. current density is calculated as follows:

    J = I/A1 = 4.3 / (0.420/100)² = 77631.9 A/m²

b. the current remains the same at both points.

c.

current density is inversely proportional to area.

that is J proportional A (or = r^2). if, the radius is increased,

the current density is decreased. so, the value of current density is smaller at A2

than A1.

d. if A2 = 3A1, the radius at A2 is,

           r₂² = 3(0.420/100)²

              r₂ = 7.2746x10^-3 m

e). current at A2 = current at A1 = 4.30 A .

f) current density = I/A2 = 4.30/(7.2746x10^-3 )2 = 25877.4 A/m2