PHY charge density 問題 高手進20點

hi, i don't regard myself as an expert, i am just a f.6 dse student who love academic exchanges

i remember clearly from my physics teacher(btw, he is a really good phy teacher) that 'number of charge carriers per unit volume' depends on material only i.e. the same material should have the same number of charge carriers per unit volume.
it can be calculated by 'number of charge carriers in 1 mole of atom/(desity of the material/molar mass of the material) '

i don't know where v = i L / NQ comes from, i usually use v = i/ nAQ...

so for Q1, i think ans 2 is correct

and for Q2, using v = i/ nAQ, increase in length does not affect v at all, so ans 1 is correct

of course, the logic in ans 1 of Q2 is correct too in my view.

personally, i think v = i L / NQ is a bit weird cuz don't take cross sectional area into account at all??as current is defined as the rate of flow of electric charges through any cross section of the conducting wire................

tell me if i am wrong^^

The number of charge per unit volume n for a given conducting material is generally constant at constant temperature.

Q1: The two equations are basically the same.
Using the same symbols as appear in the question,
v = iL/NQ
But N = nAL (n is the no. of charge per unit volume)
i.e. v = iL/nALQ = i/nAQ
The drift velocity v would thus decrease if A increases. But this must be under the condition that the current i remains constant.

The physics behind is that when A increases, the resistance of the conductor would decrease, leading to an increase of current i. To maintain the current i as before, the voltage across the conductor needs to be reduced. Since charge carriers are driven by the electric field (the strength of which depends on the applied voltage) in the conductor, the drift velocity v is proportional to the electric field strength. A reduction of voltage leads to a reduction of v.

Therefore, if the applied voltage is kept constant, then an increase of A leads to a lower resistance and hence a larger current i. This would not cause any change to the drift velocity v.

The answers from both books are correct. It only depends on the condition, whether the current i is constant or not.

Q2: As said above, the equation v = iL/NQ = i/nQA
The parameter L doesn't appear in the equation. Hence, increase of L doesn't affect the drift velocity v, under the.condition that the current i is kept constant.