A 1 \mu {C} point charge is held at the origin of a cartesian coordinate system. If a second point charge of 10 \mu {C} is moved from (0,10,0) to (5,5,5) and subsequently to (5,0,0), then the total work done is {mJ}. (Round off to 2 decimal places). Take \frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} in SI units. All coordinates are in meters.

GATE Electrical Engineering (EE) 2021 Solved Papers

Question : 33 of 65

Marks: +1, -0

1 µ {C}

point charge is held at the origin of a cartesian coordinate system. If a second point charge of

10 µ {C}

is moved from

(0,10,0)

(5,5,5)

and subsequently to

(5,0,0)

, then the total work done is

{mJ}

. (Round off to 2 decimal places). Take

\;{1}/{4 π ε_{0}}=9 × 10^{9}

in SI units. All coordinates are in meters.

Solution:

We know,

{E}

is conservative in nature, i.e.,

\ov{∇} × { {E}↖{→}=0 \& {VAB}

is independent of path taken.

{V}_{ {AB}}=-∫↙{ {A}}^{ {B}} { {E}↖{→} ⋅ {d} { {I}↖{→}

=-∫↙{A}↖{B} \;{Q_{1}}/{4 π ε_{0} r^{2}} {a}↖{∧}_{r} ⋅ d r {a}↖{∧}_{r}

=\;{ {Q}_{1}}/{4 π ε_{0}}[\;{1}/{r}]_{r=0}^{r-5}=9 × 10^{9} × 1 × 10^{-6}[\;{1}/{5}-\;{1}/{10}]

So,

W=Q_{2} V_{A B}

W=(10 × 10^{-6}) × 9 × 10^{9} × 1 × 10^{-6}[\;{1}/{5}-\;{1}/{10}]

W=9 × 10^{-2} × \;{1}/{10}=9 × 10^{-3}=9 {mJ}

Go to Question:

Prev Question

Next Question