Electrostatics Part 1

Given, mass of each spheres, m=10mg=10×10−3g
Length of thread (l)=0.5m
Separation between charges, d=0.2m
Charge of each sphere, q=‌

a

21

×10−8C
Acceleration due to gravity (g)=10ms−2
The situation can be shown as below,Taking component of tension (T)
T‌cos‌θ‌‌=mg. . . (i)
T‌sin‌θ‌‌=qE=‌

k∣q2

d2

. . . (ii)
sin‌θ=‌

d∕2

l

=‌

0.1

0.5

=‌

1

5

cos‌θ=√1−sin2θ=√1−1∕25=‌

√24

5

∴‌‌tan‌θ=‌

sin‌θ

cos‌θ

=‌

kq2

d2mg

‌‌ [using Eqs. (i) and (ii)]
⇒‌‌‌

1∕5

√24∕5

=‌

kq2

d2mg

⇒‌‌‌

1

√24

=‌

9×109×q2

(0.2)2×10×10−3×10

⇒‌‌q=√‌

(0.2)2×10−1

√24×9×109

⇒q=3×10−7C
⇒‌‌‌

a

21

×10−8=30×10−8
a=630