Rank the arrangements
Electricity and Magnetism
Level
2
The figures above show four different arrangements of three charged particles. Rank the arrangements according to the magnitude of net electrostatic force on the particle with charge
(b)>(a)>(d)>(c)
(a)=(b)>(c)>(d)
(a)>(b)>(c)=(d)
(c)>(d)>(a)>(b)
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1 solution
First, let's establish that a has strongest force. It is evident that only in (a) both charges are of same polarity so their effect on Q is "superimposed" and they don't interfere. Secondly, in case of b the -2e charge is farther away then +2e was in case a so b has the second strongest field. Now, lastly, c and d are equal because of the fact that charges have opposite polarity but same position. From the formula:
F = r 2 k q 1 q 2
if the product of charges is the same. And also the position, then the force on a charge is the same. Hence, from Coulomb's law, c and d are equivalent.
Hence, ( a ) > ( b ) > ( c ) = ( d )