Find the potential energy needed to set up a system in free space which is the form of square of mass m,2m ,3m and m of side "L"m.
Answers
Explanation:
(a)→(i) work done to bring a charge q in the electric field at a distance r
1
=q
1
V(r
1
)
(ii) work done to bring a charge q in the electric field at a distance r
2
=q
2
V(r
2
)
(iii) work done on q
2
to move it against the force of q
1
=
r
12
Kq
1
q
2
∴ The potential energy of the system =q
1
V(r
1
)+q
2
(V)(r
2
)+
r
12
Kq
1
q
2
(b) work done in moving charges = Potential of the initial position - Potential of the final position.
Now, Potential of the initial system =V
12
+V
23
+V
31
=2KQ
2
+(−3KQ
2
)+(−6KQ
2
)=−7KQ
2
J
potential energy after moving to position, A
1
,B
1
&C
1
=
1/2
K(2Q)(Q)
+
1/2
K(Q)(−3Q)
+
1/2
K(−3Q)(2Q)
=4KQ
2
−6KQ
2
−12KQ
2
=−14KQ
2
J
∴ work done =−7Q
2
K−(−14KQ
2
)=7KQ
2
J