Consider a fixed uniformly charged insulating sphere with radius R and total charge +Q . A point charge -q ( q Q ) with mass m is released from rest at a distance of 3R from the centre of the charged sphere. When the

Question

Quantrex Academy · Accepted Answer

Correct answer: D. (Qq)/(3π _0 mR)

Initial potential energy of the system when the charge

-q

is at a distance of

3R

from the centre is:

U_i = -\dfrac{1}{4\pi\epsilon_0} \dfrac{Qq}{3R}

Final potential energy of the system when the charge reaches the surface of the sphere (distance

R

from the centre) is:

U_f = -\dfrac{1}{4\pi\epsilon_0} \dfrac{Qq}{R}

According to the principle of conservation of mechanical energy:

K_i + U_i = K_f + U_f

0 - \dfrac{Qq}{12\pi\epsilon_0 R} = \dfrac{1}{2}mv^2 - \dfrac{Qq}{4\pi\epsilon_0 R}

\dfrac{1}{2}mv^2 = \dfrac{Qq}{4\pi\epsilon_0 R} - \dfrac{Qq}{12\pi\epsilon_0 R}

\dfrac{1}{2}mv^2 = \dfrac{Qq}{4\pi\epsilon_0 R} \left( 1 - \dfrac{1}{3} \right)

\dfrac{1}{2}mv^2 = \dfrac{2Qq}{12\pi\epsilon_0 R}

v^2 = \dfrac{Qq}{3\pi\epsilon_0 mR}

v = \sqrt{\dfrac{Qq}{3\pi\epsilon_0 mR}}

Answer:

\sqrt{\dfrac{Qq}{3\pi\epsilon_0 mR}}

Consider a fixed uniformly charged insulating sphere with radius R...

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