Assume that an electric field `vecE = 40x^(3)hati NC^(-1)` exists in space. The charge density at `x = 2m` is:

Options

A. `360 epsilon_(0)`, Coulmb `m^(-3)`
B. `120epsilon_(0)` Coulmb `m^(-3)`
C. `240epsilon_(0)`, Coulmb `m^(-3)`
D. `480 epsilon_(0)`, Coulmb `m^(-3)`

Answer

D

Explanation

`phi = EA`
`phi = 40x^(3)A`
`dphi = (120 x^(2)) Adx`
`dq = (dphi)epsilon_(0) = (120 epsilon_(0) x^(2)) (Adx)`
`p(x) = 120 epsilon_(0)x^(2)`
`rho(x=2) = 480 epsilon_(0)`