Electron Drift Speed: Find Current Density & Current in a Gold Wire

[kyang002]

The electron drift speed in a gold wire is 3.0 * 10^-4.

1. What is the current density in the wire?

2. What is the current if the wire diameter is 0.50 mm?

J = I / A
and I = nqva

What is the answer?

 

[ehild]

The electron drift speed in a gold wire is 3.0 * 10^-4.

1. What is the current density in the wire?

2. What is the current if the wire diameter is 0.50 mm?

J = I / A
and I = nqva

What is the answer?

You get from your formulas that the current density is J = nqv.
You should know the meaning of the letters.
n is the number of free carriers in unit volume. q is the charge of the free carriers and v is their drift speed.
Is anything you do not know from these?

ehild

 

[wais]

1. To find the current density in the wire, we can use the formula J = I/A, where J is the current density, I is the current, and A is the cross-sectional area of the wire. We can rearrange the formula to solve for I, which is the current density in this case. So, I = JA. Since we know the electron drift speed in the gold wire is 3.0 * 10^-4, we can substitute this value for v in the formula I = nqva. We also know that the charge of an electron, q, is 1.6 * 10^-19 C, and the number of electrons per unit volume, n, for gold is 5.9 * 10^28 m^-3. Finally, the cross-sectional area of the wire, A, is not given in the question, so we cannot calculate the current density without this information.

2. Similarly, we cannot calculate the current without knowing the cross-sectional area of the wire. The current, I, is equal to the product of the current density, J, and the cross-sectional area, A. So, I = JA. Without knowing the value of A, we cannot solve for I. Therefore, we need to have the cross-sectional area of the gold wire in order to calculate both the current density and the current.