Question 172: Current Electricity

Question

A cylindrical wire of radius 0.5 mm and conductivity 5 $$	imes$$ 10
7
S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x
3
$$\pi$$ mA. The value of x is _________.

Accepted Answer

We know that current density,
J = $$\sigma$$E
$$ \Rightarrow $$ J = 5 $$	imes$$ 10
7
$$	imes$$ 10 $$	imes$$ 10
$$-$$3
$$ \Rightarrow $$ J = 50 $$	imes$$ 10
4
A/m
2
Current flowing;
I = J $$	imes$$ $$\pi$$R
2
I = 50 $$	imes$$ 10
4
$$	imes$$ $$\pi$$(0.5 $$	imes$$ 10
$$-$$3
)
2
I = 5 $$	imes$$ 10
4
$$	imes$$ $$\pi$$ $$	imes$$ 0.25 $$	imes$$ 10
$$-$$6
I = 125 $$	imes$$ 10
$$-$$3
$$\pi$$
$$ 	herefore $$ x = 5

Current Electricity

A cylindrical wire of radius 0.5 mm and conductivity 5 $\times 10 7 S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x 3 \pi$ mA. The value of x is _________.

Integer / Numeric Answer Type