Question

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

according to the equation q(t) = 4t³ + 5t + 6, where t is in seconds. **(a) what is the electrical charge at (t = 2).
**(b) What is the instantaneous current through the surface at
t = 1.00 s?
**(c) What is the value of the current density? ​

Answer 1

Step-by-step 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=(dq)/(dt)\\\\I=(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=(I)/(A)\\\\J=((12t^2+5))/(0.0002)\\\\J=5000(12t^2+5)\ A/m^2`

Therefore, it is the required explanation.