A wire of radius R carries a current I.The current density is given by the function J = J₀ (1 - r/R)where r is measured from the center of the wire and J₀ is a constant.What is the value of J₀ if I = 1A,R = 1.5 mm (in A/m²)?

Question

Quizplus · Accepted Answer

We can use the formula for current density J = I/πR^2 to find J₀. Integrating the given function, we get: J = ∫(0 to R) J₀(1 - r/R)dr/πr^2 J = J₀(1/R - ln(R)/R) Setting J equal to I/πR^2 and plugging in the given values, we get: 1/π(1.5x10^-3)^2 = J₀(1/1.5x10^-3 - ln(1.5x10^-3)/1.5x10^-3) J₀ ≈ 4.24x10^10 A/m2 Therefore, the answer is D.

A Wire of Radius R Carries a Current I