5. A wire carrying 3.50 A of current has a circular cross section with a radius

Question

5. A wire carrying 3.50 A of current has a circular cross section with a radius of 2.50 mm. (a) What is the magnitude J of the current density in the wire? (b) At a certain point, a "bottleneck", the radius of the wire decreases to 0.950 mm. What is the magnitude of the current density there?

6. A wire has a square cross section with edge length 0.20 mm. If 0.031 A of current is running through it, what is the magnitude of the current density?

7. A wire has a cross-sectional area of 5.5×10-6 m2. In a time of 3.7 s, 5.8 C of charge flows through it. What is the magnitude of the current density in the wire?

Explanation / Answer

Current density = Current/Area 5) a) J = 3.5/(pi x 2.5^2 x 10^-6) = 1.78253 x 10^5 A/m^2 b) J = 3.5/(pi * 0.95^2 x 10^-6) = 1.2344 x 10^6 6) J = i/A = 0.031/(0.2*0.2 x 10^-6) = 0.775 x 10^6 7) i = Q/t = 5.8/3.7 =1.57 A J = i/A = 1.57/( 5.5×10-6 ) = 0.285 x 10^-6 . Hope you got the concept :)

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