Question

The displacement of a charge $Q$ in the electric field is $E=e_1+e_2\hat{j}+e_2\hat{k}$ is $r=a+b\hat{j}$. The work done is

• A. $Q(a{e}_1+b{e}_2)$
• B. $Q=(a{e}_1{)}^2+(b{e}_2{)}^2$
• C. $Q(e_1+e_2)a^2+b^2$
• D. $Q(e_1^2+e_2^2)(a+b)$

Answer 1

The correct option is A $Q(a{e}_1+b{e}_2)$

By using $W=Q\left(E△r\right)$
$\Rightarrow W=\left[Q\right(e_1+e_2+e_3)\cdot (a+a\hat{j}\left)\right]$
$=Q(e_{1}a+e_{2}b)$.