IB Physics SL D.2 Electric and magnetic fields questions

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Question 1

Multiple choiceHard1 mark

Two oil drops P and R have initial charges $+18Q$ and $-10Q$ where $Q>0$ They exchange charge in isolation, and afterward P has charge $+14Q$ Treat all readings as exact; $e$ is the greatest positive unit of which every initial and final charge is an integer multiple. Which pair gives $q_{R,\mathrm f}$ 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 $e$ The initial total is $(18-10)Q=+8Q$ so $q_{R,\mathrm f}=+8Q-14Q=-6Q$ The charge magnitudes $18Q, 10Q, 14Q$ and $6Q$ have greatest common unit $e=2Q$ P’s charge changes by $4Q$ so $4Q/(2Q)=2$ elementary-charge units are transferred.

B: uses $Q$ rather than the greatest common unit $2Q$ as $e$
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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