a charged belt 50cm wide travels at 30m/s between a source of charge (electrons) and a...

a charged belt 50cm wide travels at 30m/s between a source of charge (electrons) and a sphere. The belt carries charge into the sphere at a rate corresponding to 76 uA.
(a) compute the surface charge density on the belt
(b)what is the number density (number per unit area) of the electrons on the belt
I want the answer for part b

Expert Solution

Given that, w be the wide of the belt = 50 cm = 0.5 m, velocity of the belt v = 30 m/s and charge rate or current carried by the belt is I = 76 x 10^-6 A. Now, surface charge density means charge per unit area, now we can express the current in terms of w , v and . Therefore, I = wv, this expression perfectly correct in terms of dimensions also. Then, the surface charge density = I/ w v = (76 x 10^-6 A) / (0.5 m) (30 m/s) = 5.06 x 10^-6 C/m².

(b) surface density = charge q/ unit area = n e / unit area(A) since q = n e

Therefore, number density n/A = /e = (5.06 x 10^-6 C/m²) / (1.6 x 10^-19 C) = 3.16 x 10¹³

Hence number density is 3.16 x 10¹³ electrons per unit area.

genius_generous answered 2 years ago

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