Question

The quantity of charge q (in coulombs) that has passed through a surface of area 2.00 cm2 varies with time

Answer 1

Explanation:

We have,

Surface area, $A=2\ cm^2=0.0002\ m^2$

The current varies wrt time t as :

$q(t) = 4t^3 + 5t + 6$

(a) At t = 2 seconds, electrical charge is given by :

$q(t) = 4t^3 + 5t + 6\\\\q(2) = 4(2)^3 + 5(2) + 6\\\\q=48\ C$

(b) Current is given by :

$I=\dfrac{dq}{dt}\\\\I=\dfrac{d(4t^3 + 5t + 6)}{dt}\\\\I=12t^2+5$

Instantaneous current at t = 1 s is,

$I=12(1)^2+5=17\ A$

(c) Current is, $I=12t^2+5$

Current density is given by electric current per unit area.

$J=\dfrac{I}{A}\\\\J=\dfrac{(12t^2+5)}{0.0002}\\\\J=5000(12t^2+5)\ A/m^2$

Therefore, it is the required explanation.