Question

the emf provided by the battery is 12.6 V

1 Current Density and Drift Speed a) (8 pts) A group of charges, each with charge q, moves with velocity v. The number of particles per unit volume is n. What is the current density J of these charges, in magnitude and direction? Make sure that your answer has units of Alm b) (8 pts) We want to calculate how long it takes an electron to get from a car battery to the starter motor after the ignition switch is turned. Assume that the current flowing is 115 A ,and that the electrons travel through copper wire with cross-sectional area 31.2 mm2 and length 85.5 cm. What is the current density in the wire? The number density of the conduction electrons in copper is n=8.49× 1028 /m3 c) (5 pts) Given this number density and the current density, what is the drift speed of the electrons? How long does it take for an electron starting at the battery to reach the starter motor? d) (4 pts) What is the average time between collisions for an electron in this wire? The mass of the electron is m- 9.11x10-31 kg

Answer 1

(a) Let us consider a conductor of uniform area of cross - section 'A' as shown in the figure above n = number of particles per unit volume q = change on each particle v vector velocity of the particles number of particles crossing per unit time through cross - section A, N = (VA) n Therefore charge crossing per unit time through A, Q = N_q Q = navq But charge crossing per unit time is current Therefore current I = nAvq Rightarrow I/A = nqv But I/A = J is the current density Therefore J = nqv Its direction is same as that of v vector in case q is +ve and opposite to v vector in case q is -ve Therefore In vector form, J vector = n q v vector units of: n = m^-3, q = c, v = ms^-1 Therefore unit of J = m^-3 c ms^-1 = cs^-1 m^-2 = A/m^2