JEE MAIN - Physics (2021 - 24th February Evening Shift - No. 22)
A cylindrical wire of radius 0.5 mm and conductivity 5 $$\times$$ 107 S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x3$$\pi$$ mA. The value of x is _________.
Answer
5
Explanation
We know that current density,
J = $$\sigma$$E
$$ \Rightarrow $$ J = 5 $$\times$$ 107 $$\times$$ 10 $$\times$$ 10$$-$$3
$$ \Rightarrow $$ J = 50 $$\times$$ 104 A/m2
Current flowing;
I = J $$\times$$ $$\pi$$R2
I = 50 $$\times$$ 104 $$\times$$ $$\pi$$(0.5 $$\times$$ 10$$-$$3)2
I = 5 $$\times$$ 104 $$\times$$ $$\pi$$ $$\times$$ 0.25 $$\times$$ 10$$-$$6
I = 125 $$\times$$ 10$$-$$3$$\pi$$
$$ \therefore $$ x = 5
J = $$\sigma$$E
$$ \Rightarrow $$ J = 5 $$\times$$ 107 $$\times$$ 10 $$\times$$ 10$$-$$3
$$ \Rightarrow $$ J = 50 $$\times$$ 104 A/m2
Current flowing;
I = J $$\times$$ $$\pi$$R2
I = 50 $$\times$$ 104 $$\times$$ $$\pi$$(0.5 $$\times$$ 10$$-$$3)2
I = 5 $$\times$$ 104 $$\times$$ $$\pi$$ $$\times$$ 0.25 $$\times$$ 10$$-$$6
I = 125 $$\times$$ 10$$-$$3$$\pi$$
$$ \therefore $$ x = 5
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