Question

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

• A. $Q (ae_1 + be_2)$
• B. $Q \, \overline {{ae_1 } ^2 + {be_2 }^2}$
• C. $Q(e_1 + e_2)\,\, \overline{a^2 + b^2}$
• D. $Q \overline{e_1^2 + e_2^2} \,\,a + b$

Answer 1

Answer: (A)

$Q (ae_1 + be_2)$

Answer 2

By using $W = Q ( E \Delta r )$
$\Rightarrow W=Q\left[\left(e_{1}\, l+e_{2}\, j+e 3 \,k\right) \cdot(a i+b j)\right]$
$=Q\left(e_{1} a+e_{2} b\right)$