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A metal ball of radius 12cm is charged to potential 200V. A point charge 3nC is moved from infinity to a point near the ball surface. In doing so, work 100~nJ is performed. Find the distance from the final position of the charge to the ball surface. The answer should be expressed in centimeters [cm] . The ball is in a vacuum.
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Answer:
The charge of the ball with radius RR can be expresses thru its potential:
\phi_1=\frac{kq_1}{R},\\\space\\ q_1=\frac{R\phi_1}{k}.ϕ
1
=
R
kq
1
,
q
1
=
k
Rϕ
1
.
As we know, the field outside of the ball behaves as a field of a point charge.
The work done by a charge approaching from infinity in a potential field created by another charge:
W=\frac{kq_1q_2}{r},\\\space\\ r=\frac{kq_1q_2}{W}=\frac{\phi_1q_2R}{W}=0.72\text{ m}.W=
r
kq
1
q
2
,
r=
W
kq
1
q
2
=
W
ϕ
1
q
2
R
=0.72 m.
Thus, the distance to the surface of the sphere is
d=r-R=72-12=60\text{ cm}.d=r−R=72−12=60 cm.
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