Eight equal point charges each of charge 'q' and mass 'm' are placed at eight corners of a cube of side ‘a’.
(i) Find out potential energy of charge system
(ii) Find out work done by external agent against electrostatic forces and by electrostatic forces to increase all sides of cube from a to 2a.
(iii) If all the charges are released at rest, then find out their speed when they are at the corners of cube of side 2a.
(iv) If keeping all other charges fixed, charge of corner 'A' is released then find out its speed when it is at infinite distance?
(v) If all charges are released simultaneously from rest then find out their speed when they are at a very large distance from each other.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) 
(ii) W ext = – 
, W el = 
(iii) 
(iv) 
(v) 
Sol.
Electrostatic potential energy of charge system
u net = 
and by symmetry, u 1 = u 2 =u 3 = u 4 = u 5 = u 6 = u 7 = u 8
so, u net = 4 u 1 .
(i) initial potential energy = 4 
u initial = 
(ii) Potential energy of system when all sides of cube increase from a to 2a
u final = 
u final = 
Work done by external agent against electrostatic forces:
W ext = u final – u initial = – 
work done by electrostatic forces
W ele. = u initial – u final ; W ele. = 
= – W ext
(iii) By applying energy conservation between initial and final positions:
(K.E) initial + (P.E) initial = (K.E) final + (P.E) final
0 + 
v = 
(iv) ∴ At infinity P.E. of charge A = 0}
∴ By conservation of mechanical energy A & ∞
U A + K A = U ∞ + K ∞
+ 0 = 0 + 
mv 2
or v = 
(v) By energy conservation
(K.E) initial + (P.E) initial = (K.E) final + (P.E) final
0 + 
∴ v = 
m/sec
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