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**Hint:**Resistivity also known as specific electrical resistance is defined as the measure of the resistance of a given size of a particular material to electrical conduction.

Electrical resistivity is the electrical resistance per unit length and per unit of cross-sectional area at a specified temperature and is given by-

$\rho = R\dfrac{A}{l}$ where,

R is the electrical resistance of a uniform specimen of the material measured in ohms

l is the length of the piece of material measured in metres, m

A is the cross-sectional area of the specimen measured in square metres, ${m^2}$

In the given question, we will first find the area of cross-section and then put all the values in formula to find resistivity of the material.

**Complete step-by-step answer:**

Given, $R = 2\Omega $

$l = 1m$

$d = 0.4mm = 0.0004m$

First, we will find out the area of cross-section of material given by

⇒$A = \dfrac{{\pi {d^2}}}{4}$

⇒$A = \dfrac{{\pi \times {{(0.0004)}^2}}}{4}$

⇒$A = \dfrac{{3.14 \times 0.00000016}}{4}$

⇒$A = 0.0000001256$

⇒$A = 1.256 \times {10^{ - 7}}{m^2}$

Now, we need to find the resistivity of the material.

We know, $\rho = R\dfrac{A}{l}$

Putting in the values in formula, we get

$\rho = \dfrac{{2\Omega \times 1.256 \times {{10}^{ - 7}}{m^2}}}{{1m}}$

⇒$\rho = 2.514 \times {10^{ - 7}}\Omega m$

Hence, the resistivity of the material is $2.514 \times {10^{ - 7}}\Omega m$

**Option B is correct.**

**Note:**The resistivity of a material can also be defined in terms of the magnitude of the electric field across it that gives a certain current density. It is possible to devise an electrical resistivity formula which is given by-

$\rho = \dfrac{E}{J}$ where,

ρ is the resistivity of the material.

E is the magnitude of the electric field.

J is the magnitude of the current density.

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