Question

A charge +q is revolving around a stationary charge +Q of radius r if force b/w carge is F then work done of this motion will be?​

Answer 1

Answer:

Given:

+q charge is revolving around a charge +Q in a radius "r". Force between the charge is F

To find:

Work done by the revolving charge in this kind of motion.

Concept:

Work done by any force is given as the dot product of Force and Displacement.

Mathematically,

$\boxed{ \sf{ \large{work = \vec F. \: \vec r}}}$

$\sf{ \implies \: work = f \times r \times \cos( \theta)}$

Now in a circular motion , the force vector and the displacement vector is at 90° with another with one another.

We know that cos (90°) = 0

$\sf{ \implies \: work = f \times r \times \cos( 90 \degree)}$

$\sf{ \implies \: work = f \times r \times ( 0)}$

$\sf{ \implies \: work = 0 \: joules}$

So , no work is done .

Answer 2

$\blue{\underline{ \huge{ \blue{\boxed{ \mathfrak{\fcolorbox{red}{orange}{\purple{Answer\: :-}}}}}}}} \\ \\ \star \rm \: \red{Given} \\ \\ \implies \rm \: a \: charge \: + q \: is \: revolving \: around \: stationary \\ \rm \: charge \: + Q \: of \: radius \: r \: and \: force \: between \: them \: is \: F \\ \\ \star \rm \: \red{To \: Find} \\ \\ \implies \rm \: net \: work \: done \: in \: this \: type \: of \: circular \: motion \\ \\ \star \rm \: \red{Formula} \\ \\ \implies \rm \: net \: work \: done \: in \: any \: kind \: of \: motion \: is \: \\ \rm \: mathematically \: given \: by... \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{\boxed{ \bold{ \pink{ \sf{W = \vec{F} \: {\tiny{ \bullet}} \: \vec{d}}}}}} \\ \\ \implies \rm \: it \: means \: that \: work \: done \: is \: dot \: product \: of \\ \rm \: force \: and \: displacement... \\ \\ \implies \rm \: dot \: multipication \: between \: two \: quntities \\ \rm is \: given \: by... \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \bold{ \pink{ \sf{ \vec{A} \: { \tiny{ \bullet}} \: \vec{B} = AB \cos\theta}}}}} \\ \\ \implies \rm \: where \: \theta = angle \: between \: two \: vectors \\ \\ \star \rm \: \red{Solution} \\ \\ \implies \rm \: here \: angle \: between \: Force \: and \: displacement \\ \rm \: is \: 90 \degree \\ \\ \implies \rm \: and \: we \: know \: that \: cos90 \degree = 0 \\ \\ \therefore \: \boxed{ \boxed{ \orange{ \bold{ \rm{W{ \tiny{net}} = 0 \: J}}}}}$