Question

The drift velocity of free electron in a conducting wire carrying current I is v. If in a wire of same metal but double the radius the current will be 2I then the drift velocity of electrons will be?

Answer 1

Answer:

Drift velocity is halved

Explanation:

The mathematical expression for drift velocity is ;

Current =   n A v Q

V = 1 / nAQ

Here n is the number of electrons per cubic metre

A the cross sectional area

v is the drift velocity

Q is the electronic charge

V = 1 / nAQ

Here drift velocity is directly proportional to current but inversely proportional to area. SO if radius is doubles, it means area is increased 4 times, and current is doubled that is;

V’ = 2l / nq x 4A;

V’= ½ V

Hence drift velocity is halved

Answer 2

Drift velocity is halved

Explanation:

We can calculate drift velocity using the formula, Current I =   n A v Q

So we get V = I / nAQ

Where n is the number of electrons per cubic metre, A is the cross sectional area, V is the drift velocity and Q is the electronic charge.

We find that drift velocity is directly proportional to current but inversely proportional to area.

Now, give that the wire is double the radius and current is 2I.

Substituting the values to find change in drift velocity:  

Cross sectional area of the wire = pi*R² = pi*2R² = 4 (pi*R²) = 4 (area of the first wire) = 4A  

So V’ = 2l / n * 4A * Q

V’= ½ V

Thus we infer that drift velocity is halved when radius is doubled and current is 2I.