Physics - Electrostatics Question with Solution | TestHub

PhysicsElectrostaticsElectric Field & ForceHard2 minPYQ_2016

PhysicsHardsingle choice

Two identical charged spheres suspended from a common point by two massless strings of lengths I, are initially at a distance d $(d << 1)$ 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:

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Answer:

Solution:

From figure $tan θ = \frac{F _{e}}{mg} ≃ θ$ $\frac{kq ^{2}}{x ^{2} mg} = \frac{x}{2 ℓ}$ or $x^{3} \propto q^{2} \dots$ (1) or $x^{3/2} \propto q \dots (2)$ Differentiating eq. (1) w.r.t. time $3 x^{2} \frac{dx}{dt} \propto 2 q \frac{dq}{dt}$ but $\frac{dq}{dt}$ is constant $so x^{2} (v) \propto q Replace q from eq. (2)$ $x^{2} (v) \propto x^{3/2}$ or $v \propto x^{- 1/2}$

Stream:BITSATSubject:PhysicsTopic:ElectrostaticsSubtopic:Electric Field & Force

⏱ 2mℹ️ Source: PYQ_2016

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