Question

The drift velocity of electrons in a wire of radius r is proportional to

(a) r 

(b) r² 

(c) r³

(d) none of the above

Answer 1

(d) none of the above

Answer 2

We know that \(I=neAV_d\) , if we rewrite the equation in terms of drift velocity we get \(V_d=\frac{I}{neA}\) and what is A, A is nothing but the area of cross section which is the area of the circle i.e \(A=\pi r^2\), put this vaule in above equation of drift velocity, we get- \(V_d=\frac{I}{ne\pi r^2}\), so we see that drift velocity is inversely proportional to the square of the radius. 

So the required answer is option (d). 

Read more about derivation for drift velocity in detail.