The displacement of a charge Q in the electric field E=e1 1+e2 j+e3 k is r=a i+b j. The work done is

Question

The displacement of a charge Q in the electric field E=e1 1+e2 j+e3 k is r=a i+b j. The work done is (A) Q (ae1 + be2) (B) Q overline ae1 2 + be2 2 (C) Q(e1 + e2) overlinea2 + b2 (D) Q overlinee12 + e22 a + b

Tardigrade Admin · Accepted Answer

By using W = Q ( E Δ r ) ⇒ W=Q[(e1 l+e2 j+e 3 k) ⋅(a i+b j)] =Q(e1 a+e2 b)

Q. The displacement of a charge $Q$ in the electric field $E = e_{1} 1 + e_{2} j + e_{3} k$ is $r = ai + bj$ . The work done is

$Q (a e_{1} + b e_{2})$

$Q \overline{a e_{1}^{2} + b e_{2}^{2}}$

$Q (e_{1} + e_{2}) \overline{a^{2} + b^{2}}$

$Q \overline{e_{1}^{2} + e_{2}^{2}} a + b$

By using $W = Q (E Δ r)$
$\Rightarrow W = Q [(e_{1} l + e_{2} j + e 3 k) \cdot (ai + bj)]$
$= Q (e_{1} a + e_{2} b)$

Q. The displacement of a charge Q in the electric field E=e1​1+e2​j+e3​k is r=ai+bj. The work done is

Q(ae1​+be2​)

Qae1​2+be2​2​

Q(e1​+e2​)a2+b2​

Qe12​+e22​​a+b