What is the drift velocity of the electron in a silver wire of length 1m area, of cross-section 3.14*10^-6 sq.m & carrying a current of 10 Ampere ?

Given, density of silver = 10.5*10^3 Kg m^-3.

To find the drift velocity of electrons in a silver wire, we can use the formula that relates current, charge, number density of charge carriers, and drift velocity. The formula is given by:

Drift Velocity Formula

The drift velocity (v_d) can be calculated using the equation:

I = n * A * e * v_d

Where:

• I = current (in Amperes)
• n = number density of charge carriers (in m^-3)
• A = cross-sectional area of the wire (in m²)
• e = charge of an electron (approximately 1.6 x 10^-19 Coulombs)
• v_d = drift velocity (in m/s)

Step 1: Calculate the Number Density of Electrons

First, we need to find the number density (n) of electrons in silver. The number density can be calculated using the formula:

n = (density of silver) / (molar mass of silver) * Avogadro's number

The molar mass of silver (Ag) is approximately 107.87 g/mol, which is 0.10787 kg/mol. Avogadro's number is about 6.022 x 10²³ particles/mol.

Now, substituting the values:

n = (10.5 x 10³ kg/m³) / (0.10787 kg/mol) * (6.022 x 10²³ mol^-1)

Calculating this gives:

n ≈ 5.84 x 10²⁸ electrons/m³

Step 2: Rearranging the Drift Velocity Formula

Now that we have the number density, we can rearrange the drift velocity formula to solve for v_d:

v_d = I / (n * A * e)

Step 3: Substitute the Values

We know:

• I = 10 A
• A = 3.14 x 10^-6 m²
• e = 1.6 x 10^-19 C
• n ≈ 5.84 x 10²⁸ electrons/m³

Substituting these values into the drift velocity equation:

v_d = 10 / (5.84 x 10²⁸ * 3.14 x 10^-6 * 1.6 x 10^-19)

Step 4: Calculate the Drift Velocity

Now, let's calculate the denominator:

n * A * e ≈ 5.84 x 10²⁸ * 3.14 x 10^-6 * 1.6 x 10^-19 ≈ 2.93 x 10⁴

Now we can find v_d:

v_d ≈ 10 / (2.93 x 10⁴) ≈ 3.41 x 10^-5 m/s

Final Result

The drift velocity of the electrons in the silver wire is approximately 3.41 x 10^-5 m/s. This value illustrates how slowly electrons drift through a conductor, even when a significant current is flowing.