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Question

A cylindrical wire of radius 0.5mm and conductivity 5×107S/m is subjected to an electric field of 10mV/m. The expected value of current in the wire will be x3πmA. The value of x is ____.


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Solution

Step 1: Given Data:

Radius of wire R=0.5mm

=5×10-4m

Conductivity σ=5×107S/m

Electric field E=10mV/m

=10×10-3V/m

Expected value of current =x3πmA

Step 2: Calculating the current density:

Current density J is given as,

J=σE

Where, σ= Conductivity of material

E=Electric field

J=5×107×10×10-3

=5×105A/m2

Step 3: Calculating the expected current:

Current density J=currentareaofcrosssection

current=J×πR2

=5×105×π×5×10-42

=125π×10-3A

=53π×10-3A

=53πmA

Now, comparing the value of expected current value of xis found to be 5.

Hence, value of xis 5.


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