Answer:
r = 0.303m
= 30.3cm
Explanation:
Given that,
The number of electrons transferred from one sphere to the other,
n =
1
×10
¹³e
le
c
t
r
o
n
s
The electrostatic potential energy between the spheres,
U
=
−
0.061
J
The charge on an electron,
q
=
−
1.6
×
10
⁻¹⁹C
The coulomb constant,
K
=
8.98755
×
10
⁹
N
⋅
m
²
/
C
2²
Due to the transfer of electrons, both spheres become equally and oppositely.
The charge gained by the sphere due to the excess of the electron is:
q
₁ =
n
q
=
1
×10
¹³ * −
1.6
×
10
⁻¹⁹
= -1.6 × 10⁻⁶C
The charge left on the first sphere is =
q
₂ = -q₁ = 1.6 × 10⁻⁶C
The electric potential energy between two point charges is given by the following equation:
U
=
K
q
₁q
₂/r
q
₁ and q
₂ are the two charges.
r is the distance between the charge and the point.
K = 8.98755 × 10
⁹
N
⋅
m
²
/
C
²
we have:
-0.061 = (8.98755 × 10
⁹ * (-1.6 × 10⁻⁶)²) / r
r = (18.41 × 10
⁻³) / 0.061
r = 0.303m
= 30.3cm
