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MMLU-Pro / 10115 / The initial charges on the three identical metal spheres in Fig. 21-24 are the…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

The initial charges on the three identical metal spheres in Fig. 21-24 are the following: sphere A,QA, Q; sphere B,−Q/4B,-Q / 4; and sphere C,Q/2C, Q / 2, where Q=2.00×10−14Q=2.00 \times 10^{-14} C. Spheres AA and BB are fixed in place, with a center-to-center separation of $d=1.20 \mathrm{~m}$, which is much larger than the spheres. Sphere CC is touched first to sphere AA and then to sphere BB and is then removed. What then is the magnitude of the electrostatic force between spheres AA and BB ?
Plain-text mathematical notation (without MathML)
The initial charges on the three identical metal spheres in Fig. 21-24 are the following: sphere A,Q; sphere B,−Q/4; and sphere C,Q/2, where Q=2.00×10^(−14) C. Spheres A and B are fixed in place, with a center-to-center separation of $d=1.20 \mathrm{~m}$, which is much larger than the spheres. Sphere C is touched first to sphere A and then to sphere B and is then removed. What then is the magnitude of the electrostatic force between spheres A and B ?
Original LaTeX notation
The initial charges on the three identical metal spheres in Fig. 21-24 are the following: sphere $A, Q$; sphere $B,-Q / 4$; and sphere $C, Q / 2$, where $Q=2.00 \times 10^{-14}$ C. Spheres $A$ and $B$ are fixed in place, with a center-to-center separation of $d=1.20 \mathrm{~m}$, which is much larger than the spheres. Sphere $C$ is touched first to sphere $A$ and then to sphere $B$ and is then removed. What then is the magnitude of the electrostatic force between spheres $A$ and $B$ ?

category

physics

options

  1. $2.50 \times 10^{-19} \mathrm{~N}$
  2. $7.35 \times 10^{-19} \mathrm{~N}$
  3. $4.68$ $10^{-19} \mathrm{~N}$
  4. $5.97 \times 10^{-19} \mathrm{~N}$
  5. $5.80 \times 10^{-19} \mathrm{~N}$
  6. $8.14 \times 10^{-19} \mathrm{~N}$
  7. $6.42 \times 10^{-19} \mathrm{~N}$
  8. $3.20 \times 10^{-19} \mathrm{~N}$
  9. $9.81 \times 10^{-19} \mathrm{~N}$
  10. $1.56 \times 10^{-19} \mathrm{~N}$

src

scibench-fund

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Source and history

upstream_id / Original problem ID
10115
task_id
de027f68-3aba-5e68-adb5-baeb2999cdc5
task_key
default--test--10115
task_revision_id
1
config / split
default / test

Official source

initial import