A current flows in a wire of circular cross-section with the free electrons travelling with a mean drift velocity v. If an equal current flows in a wire of the same material but of twice the radius,what is the new mean drift velocity (a)v/4(b)v/2(c)2v(d)4v
radius*2 means area*4, so v/4
V/4
V/2
To determine the new mean drift velocity, we can use the equation for the current density (J) in a wire:
J = n * e * v
Where:
- J is the current density
- n is the number density of free electrons
- e is the charge of each electron
- v is the mean drift velocity
Since the current is the same in both wires, we can equate the current densities:
J₁ = J₂
In terms of the given variables:
n₁ * e * v₁ = n₂ * e * v₂
Since both wires are made of the same material, the number density of free electrons (n) will remain the same. Also, the charge of each electron (e) remains constant. Therefore, we can simplify the equation to:
v₁ = v₂
This means that the new mean drift velocity (v₂) will be the same as the original mean drift velocity (v₁).
Thus, the correct answer is (a) v/4.