Electrostatics Question 221
Question: Two equally charged, identical metal spheres A and B repel each other with a force ‘F’. The spheres are kept fixed with a distance ‘r’ between them. A third identical, but uncharged sphere C is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is [UPSEAT 2004; DCE 2005]
Options:
A) F
B) 3F/4
C) F/2
D) F/4
Show Answer
Answer:
Correct Answer: A
Solution:
Initially $ F=k\frac{Q^{2}}{r^{2}} $ ……. (i)
Finally Force on C due to A, $ F _{A}=\frac{k{{(Q/2)}^{2}}}{{{(r/2)}^{2}}}=\frac{kQ^{2}}{r^{2}} $
Force on C due to B, $ F _{B}=\frac{KQ(Q/2)}{{{(r/2)}^{2}}}=\frac{2KQ^{2}}{r^{2}} $
Net force on C, $ F _{net}=F _{B}-F _{A}=\frac{kQ^{2}}{r^{2}}=F $
