Calculate the displacement current density when the electric flux density is 20sin 0.5t.

To calculate the displacement current density ((J_d)) when the electric flux density ((D)) is given by (D = 20sin(0.5t)), we’ll make use of Maxwell’s displacement current concept. The displacement current density can be found using the equation:

[

J_d = frac{dD}{dt}

]

Given that (D = 20sin(0.5t)), let’s differentiate it with respect to (t):

[

frac{dD}{dt} = 20cos(0.5t) times 0.5 = 10cos(0.5t)

]

So, the displacement current density, (J_d), is:

[

J_d = 10cos(0.5t)

]

This expression provides the displacement current density as a function of time.