Question 927: Electrostats & Capacitance

Question

Two identical charged  spheres suspended  from a common  point by two massless strings of lengths $$l$$, are initially at a distance d(d < < $$l$$) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as

Accepted Answer

From figure $$	an 	heta  = {{{F_e}} \over {mg}} \simeq 	heta $$
$${{k{q^2}} \over {{x^2}mg}} = {x \over {2\ell }}$$
$$ \Rightarrow $$ $${x^3} \propto {q^2}$$   ...(i)
$$ \Rightarrow {x^{3/2}} \propto q$$
Differentiating eq. (1) w.r.t. time
$$3{x^2}{{dx} \over {dt}} \propto 2q{{dq} \over {dt}}$$ but $${{dq} \over {dt}}$$ is constant
so x
2
(v) $$ \propto $$ q Replace q from eq. (2)
x
2
(v) $$ \propto $$ x
3/2
$$ \Rightarrow $$ v $$ \propto $$ x
Ã¢ÂÂ1/2

Answer

v $$ \propto $$ x$$-$$1/2

Answer

v $$ \propto $$ x$$-$$1

Answer

v $$ \propto $$ x1/2

Answer

v $$ \propto $$ x

Electrostats & Capacitance

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