Question

A region contains a uniform electric field $E=(10\hat{i}+30\hat{j})V{m}^{-1}\cdot A$ and $B$ are two points in the field at $(1,2,0)m$ and $(2,1,3)m$, respectively. The work done when a charge of $0.8C$ moves from $A$ to $B$ in a parabolic path is

• A. 8 J
• B. 80 J
• C. 40 J
• D. 16 J

Answer 1

Answer: (D)

Electric field, $E=(10\hat{i}+30\hat{j})V/m$
The coordinates of $A$ and $B$ are $(1,2,0)$ and $(2,1,3)$.
$\therefore r_A=\hat{i}+2\hat{j}+0$
$r_B=2\hat{i}+\hat{j}+3\hat{k}$
Displacement, $dr=r_B-r_A$
$=(2\hat{i}+\hat{j}+3\hat{k})-(\hat{i}+2\hat{j})$
$=\hat{i}-\hat{j}+3\hat{k}$
We know $E=\frac{dV}{dr}$
$\Rightarrow dV=E\cdot dr$
$=(10\hat{i}+30\hat{j})\cdot (\hat{i}-\hat{j}+3\hat{k})$
$=10\hat{i}\cdot \hat{i}-30\hat{j}\cdot \hat{j}+0$
$=10-30=-20$
$=q\times |dV|$
Work done, $W=q\cdot 8C$
Here, $q=0.8(20)=16$ joule $=16J$