Charge between Charges
Electricity and Magnetism
Level
3
Two charges of magnitude +4e and +e are kept at a distance from each other. What charge should be kept in between them to make the system stable?
+e
-e
-2e
The charge can't be in between them to make the system stable
Any charge irrespective of magnitude and nature
+2e
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1 solution
We want to use Coulomb's Law of Electrostatic Forces: F = r 2 k q 1 q 2 . Let us consider placing a charge Q in between our + e and + 4 e charges such that it's at distance x and r − x from either of our given charges. Now let's apply the following force equality:
F Q , e = F Q , 4 e ⇒ x 2 k ( e ) ( Q ) = ( r − x ) 2 k ( 4 e ) ( Q ) ⇒ x 2 1 = ( r − x ) 2 4 ⇒ r − x = ± 2 x ⇒ x = 3 r , − r .
If we only admit the positive solution x = 3 r , then Q is contained in between our initial charges. Our result also shows that this new system is in equilibrium irrespective of Q ′ s magnitude and nature as well! Choice F is correct.