Your No.s 3/21/20118 Test l KSU ID.. Full name 2 (8 points) The quantity of char

Question

Your No.s 3/21/20118 Test l KSU ID.. Full name 2 (8 points) The quantity of charge g (in coulombs) that has of area 2 cm2 varies with time according to the equation seconds. q2+5, where t is in a) What is the instantaneous current through the surface at b) What is the value of the current density in A/m2? 1 s? 3. (4 poists) A curent density of 450 x 10-13 A/m2 exists in the atmosphere at a location where the electric field is 187 V/m. Calculate the electrical conductivity of the Earthi's atmosphere in this region.

Explanation / Answer

2A.

Current is given by:

i = dq/dt

q = t^3 + 2t + 5

dq/dt = d(t^3 + 2t + 5)/dt

dq/dt = 3t^2 + 2*1 + 0

i = 3t^2 + 2

At t = 1 sec

i(1) = 3*1^2 + 2 = 5 Amp

Part B

Current density is given by:

J = Current/Surface area

Surface area = 2 cm^2 = 2*10^-4 m^2

J = (3t^2 + 5)/(2*10^-4)

J = (1.5*t^2 + 2.5)*10^4 A/m^2

J = (15000t2 + 25000) A/m2

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