Consider a wire of a circular cross-section with a radius of R = 3.17 mm. The magnitude of the current density is modeled as J = cr2 = 9.00 ✕ 106 A/m4 r2. What is the current (in A) through the inner section of the wire from the center to r = 0.5R?

The current is  

Explanation:

From the question we are told that

     The  radius is

      The current density is  

      The distance we are considering is  

Generally current density is mathematically represented as

Where A is the cross-sectional area represented as

=>      

=>    

Now the change in current per unit length is mathematically evaluated as

Now to obtain the current (in A) through the inner section of the wire from the center to r = 0.5R we integrate dI from the 0 (center) to point 0.5R as follows

substituting values

resonant frequency