Question 1

Multiple choiceHard1 mark

Two oil drops P and R have initial charges +18Q+18Q and −10Q-10Q where Q>0Q>0 They exchange charge in isolation, and afterward P has charge +14Q+14Q Treat all readings as exact; ee is the greatest positive unit of which every initial and final charge is an integer multiple. Which pair gives qR,fq_{R,\mathrm f} and the number of elementary-charge units transferred? [1]

Show answer and explanation

Answer: A [1]. The total charge of the isolated pair is conserved, and each drop’s charge is an integer multiple of ee The initial total is (18−10)Q=+8Q(18-10)Q=+8Q so qR,f=+8Q−14Q=−6Qq_{R,\mathrm f}=+8Q-14Q=-6Q The charge magnitudes 18Q,10Q,14Q18Q, 10Q, 14Q and 6Q6Q have greatest common unit e=2Qe=2Q P’s charge changes by 4Q4Q so 4Q/(2Q)=24Q/(2Q)=2 elementary-charge units are transferred.

B: uses QQ rather than the greatest common unit 2Q2Q as ee
C: gives the residual charge the wrong sign.
D: assigns R the same signed change as P, rather than the opposite change required by conservation.

Remember: in an isolated pair, the signed charge changes sum to zero.

Total: 1 mark.

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