Question

Two identical He-filled spherical balloons each carrying a charge q are tied to a weight W with strings and float in equlibrium, as shown in figure.
(i) Find the magnitude of q, assuming that the charge on each balloon acts as if it were concentrated at the center.
(ii) Find the volume of each balloon. Take the density of He as `rho_(He)` and the density of air as `rho_(a)`. Ignore the weight of the unfilled balloons .
,

Answer 1

(i) `2T cos theta =W, T sin theta=F`
or `(tan theta)/(2)=F/W or F=W(tan theta)/2`
or, `(q^2)/(4 pi epsilon_(0)(2x)^(2))=(W tan theta)/(2)` or `q=sqrt(8W tan theta pi epsilon_(0)x^(2))`
(ii) `T cos theta+mg=B implies (W)/(2) + V(rho_(He))g=Vrho_(a)g`
or `V=(W)/(2(rho_(a)-rho_(He))g)`.