Consider a uniform cylindrical conductor of length L and cross-sectional area A containing n free electrons per unit volume, each with elementary charge e. The conductor is connected to an ideal battery of emf ε, completing a closed circuit that includes only the conductor and ideal connecting leads of negligible resistance. The temperature is held constant so that the conductor’s resistance R does not change.
(a) Starting from fundamental definitions, derive an algebraic expression for the steady drift speed vd of the free electrons in the conductor in terms of ε, L, A, n, e, and R.
(b) Using your result from part (a), explain qualitatively how vd would change if the emf of the battery were doubled while all other parameters remained the same.
(c) Suppose the conductor is replaced with a second conductor of identical material and length but half the cross-sectional area. Predict quantitatively how the new drift speed compares with the original drift speed when both conductors are connected to the same battery emf ε.