The displacement r of a charge Q in an electric field`vec E = c_(1) hat i + c_(2) hat j + c_(3)hat k ` is ` vec r = a hat I + b hat j` .The work done is

Options

A. `Q(ac_(1) + bc_(2))`
B. `Qsqrt((ac_(1))^(2) + (bc_(2))^(2))`
C. `Q(c_(1) + c_(2)) sqrt(a^(2) + b^(2))`
D. `Q(sqrt(c_(2)^(2)+ c_(1)^(2))(a +b)`

Answer

(a)

Explanation

Work done by an electric field,
`W = vec F .Vec r`
` = Q vecE.vec r`
`= Q[(c_(1) hat i) +C_(2) hat j + c_(3) hat k).(a hat I + b hat j)] = Q(c_(1)a + c_(2)b)`