Electrostatics 7 Question 3

3. There is uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed v[R(t)] of the distribution as a function of its instantaneous radius R(t) is

(Main 2019, 12 Jan I) (a)

(c)

(b)

(d)

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Solution:

  1. Key Idea As, electrostatic force is conserved in nature so, total energy of charge distribution remains constant in absence of any external interaction.

Let radius of distribution at some instant t is R. At t=0, radius is given R0

Now by conservation of energy, we have

0+kQ22R0=12mv2+kQ22R

( The distribution starts from rest, so, initial kinetic energy is zero.)

Differentiating this equation with respect to R, we get

12m2vdvdRkQ22R2=0 or dvdR=kQ22mvR2

Here, dvdR= slope of v versus R graph. It decreases with increasing v and R.

Also, slope 0 as R.

From above conclusions, we can see that the best suited graph is given in option (c).



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