P27_005.PDF

5. (a) The magnitude of the current density is given by J = nqv d ,where n is the number of particles per

unit volume, q is the charge on each particle, and v d is the drift speed of the particles. The particle

concentration is n =2 . 0

10 8 / cm 3 =2 . 0

10 14 m − 3 , the charge is q =2 e =2(1 . 60

10 − 19 C) =

3 . 20

10 − 19 C, and the drift speed is 1 . 0

10 5 m / s. Thus,

J =(2

10 14 / m)(3 . 2

10 − 19 C)(1 . 0

10 5 m / s) = 6 . 4A / m 2

Since the particles are positively charged the current density is in the same direction as their motion,

to the north.

(b) The current cannot be calculated unless the cross-sectional area of the beam is known. Then i = JA

can be used.