A cylindrical wire of radius 0.5 mm and conductivity 5 × 1 0 7 S m − 1 is subjected to an electric field of 10 mV m − 1 . The expected value of current in the wire will be x 3 π mA . The value of x is

Question

A cylindrical wire of radius 0.5 mm and conductivity 5 × 1 0 7 S m − 1 is subjected to an electric field of 10 mV m − 1 . The expected value of current in the wire will be x 3 π mA . The value of x is _________.

TestHub · Accepted Answer

Conductivity σ = 5 × 1 0 7 S m − 1 Radius r = 0.5 mm = 5 × 1 0 − 4 m E = 10 × 1 0 − 3 V m − 1 J = σ E = 10 × 1 0 − 3 × 5 × 1 0 7 ⇒ J = 5 × 1 0 5 ⇒ A i ​ = 5 × 1 0 5 i = 5 × 1 0 5 × π r 2 = 5 × 1 0 5 × π × ( 5 × 1 0 − 4 ) 2 = 125 π × 1 0 − 3 A Therefore, i = 125 π mA Hence, x = 5

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