Explanation:
We have,
Surface area, [tex]A=2\ cm^2=0.0002\ m^2[/tex]
The current varies wrt time t as :
[tex]q(t) = 4t^3 + 5t + 6[/tex]
(a) At t = 2 seconds, electrical charge is given by :
[tex]q(t) = 4t^3 + 5t + 6\\\\q(2) = 4(2)^3 + 5(2) + 6\\\\q=48\ C[/tex]
(b) Current is given by :
[tex]I=\dfrac{dq}{dt}\\\\I=\dfrac{d(4t^3 + 5t + 6)}{dt}\\\\I=12t^2+5[/tex]
Instantaneous current at t = 1 s is,
[tex]I=12(1)^2+5=17\ A[/tex]
(c) Current is, [tex]I=12t^2+5[/tex]
Current density is given by electric current per unit area.
[tex]J=\dfrac{I}{A}\\\\J=\dfrac{(12t^2+5)}{0.0002}\\\\J=5000(12t^2+5)\ A/m^2[/tex]
Therefore, it is the required explanation.
