Question

Example 16. Two identical charged spheres each of mass 100 g are suspended in air by two strings
of length 100 cm and make an angle of 2theta with each other. Due to repulsion, the spheres remain at a distance from each other. Find the charge on each sphere. What will happen if the system is taken to a
free space (say a satellite)?

Answer 1

Answer:

The will repel there also

Explanation:

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Answer 2

Given :

m = 100 g = 0.1 kg

l = 100 cm = 1 m

θ = 2

To find:

q =?

Explanation:

The length of a string is 1 m having tension T.

from fig.

Tcosθ = mg       ...(1)

Tsinθ = $\frac{k\ q^2}{(2\ l\ sin\theta)^2}$     ...(2)

Divide eq (2) by eq ( 1 ) & we get

$\displaystyle tan \theta = \frac{kq^2}{(2l \times\frac{1}{\sqrt{2} })^2 } \ mg$

$\displaysyle {q^2 = \frac{2l^2mg}{k} }$

Put the values in the above equation

$q^2 = \frac{tan 2 \times 2 \times1 \times 1 \times 0.1 \times 9.91}{9 \times 10^9}$

q= 0.087 $10^{-9$ C

∴ q= 0.09 μC

If the system is taken to free space then $\displaystyle \epsilon = \epsilon_0$

But $\displaystyle \epsilon =k \ \epsilon_0 = 8.85 \imes 10^{-12 } \ k$

The relative permittivity becomes k times than vacuum permittivity.  

Prefer the following fig