Question

the quantity of charge q (in coulombs) that has passed through a surface of area 2.00 cm^2 varies with time according to the equation q=4t^3 + 5t+6 , where t is in seconds.a)what is the instantaneous current through the surface at t=1.00 s? b)what is the value of the current density?

Answer 1

a)

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

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

b)

$$J(1)=\frac{I(1)}{A}=\frac{17}{2\cdot 10^{-4}}=85000\frac{A}{m^2}$$