Question

A region contains a uniform electric field $E =(10 \hat{ i }+30 \hat{ j }) Vm ^{-1} \cdot A$ 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 $0.8\, C$ 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, $d r=r_{B}-r_{A}$
$=(2 \hat{ i }+\hat{ j }+3 \hat{ k })-(\hat{ i }+2 \hat{ j }) $
$=\hat{ i }-\hat{ j }+3 \hat{ k } $
We know $E =\frac{d V}{d r} $
$ \Rightarrow d V =E \cdot d r $
$=(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|d V| $
Work done, $ W =q \cdot 8 C $
Here, $q=0.8(20)=16 $ joule $=16 \,J$