find the work done by an external agent in slowly shifting a charge `q = 1 mu C` in the electric field ` vec E = 10^3 hat i Vm^-1` from the point `P(1,2) "to" Q(3, 4)`.

Options

A. `2 xx 10^(-3) J`
B. `4xx 10^(-3) J`
C. `-2 xx 10^(-3) J`
D. `-4 xx 10^(-3) J`

Answer

C

Explanation

The work done against the electric field is
`W = -q underset(1)overset(2)int vecE. Vecdl = -q int (Ehati).(dx hati + dy hatj)`
`=-q underset(x_(1))overset(x_(2))int E dx`
`=-qE(x_(2) - x_(1))`
`=-(10^(-6)) (10^(3) V//m)(3 -1)`
`=-2 xx 10^(-3) J`